The topic of Part II is the human mind, the knowledge of which, together with that of God, is necessary to attain blessedness.  The argument of this part can be divided into 4 main sections.
1) definitions and axioms
2) The nature of the mind and its relation to the body (Prop 1-15)
3) the intellect and the extent of human knowledge (16-47)
4) the will, its alleged freedom and its relation to the intellect. (48-9)
Here we do only 1,2 and 4.

A. Definitions and axioms

Def. 1: the point here is that a body is a mode of God as extended.
Def. 2: the point is that the essence of a thing X is the necessary and sufficient condition of X.
At IIp10note, S explains why he does not say that the essence of a thing is that without which the thing cannot be or be conceived (otherwise God would belong to the essence of everything)
Def. 3: "By idea, I mean the mental conception which is formed by the mind as a thinking thing"
As S explains, he emphasizes the activity of the mind in conceiving objects.  It turns out that for S. to have an idea is to conceive of something, or to have a belief about it, not merely to have a mental picture or mental description of it. (see IIp49)
Def. 4: an adequate idea is one which has all the intrinsic properties of a true idea.  The extrinsic properties of a true idea is the agreement with its ideatum. S doesn't explain what the intrinsic properties are. Probably what he has in mind is that an idea is adequate if it is possible to deduce from it the ideas of the properties of the ideatum. Example: the idea of triangle.
For S, all adequate ideas are true and vice versa.
Def. 5: Duration is the indefinite continuation of a thing.  That is, attributing duration to something says nothing about how long it exists.
Def. 6: by reality and perfection I mean the same thing.
Def. 7: the point is that an individual thing is a finite thing with determinate existence.

Axioms

Ax. 1: the essence of man doesn't involve existence: any man could not exist.
Ax. 2: man thinks
Ax. 3: The point here is that the modes of thinking, e.g., love, desire (the emotions), presuppose the idea of the object of the emotion but not vice versa.
Ax. 4: We feel a certain body to be affected in many ways.
Ax. 5: We do not feel or perceive any individual thing except bodies and modes of thinking.
 

B. The nature of the mind and its relation to the body (1-15).

Props. 1 &2: Thought and extension are attributes of God, since God has all the attributes.
Prop. 3: "In God there is necessarily the idea not only of his essence, but also of all things which necessarily follow from his essence.
The idea behind the proof is that since thought is an infinite attribute of God expressing God's essence, in God there must be the    idea of what flows from that essence.
In sum, in God there is an idea for every thing.
Prop. 4: The idea of God is one since God is one.
Props 5-6: The point here is that each attribute is a closed causal system, since each attribute is conceived through itself, and consequently nothing in it can be caused by what is outside the attribute.
NOTE: This is an implicit attack on Descartes' interactionism.
In the note, S. attacks the view that extended things are created because God has ideas of them.
Prop. 7: "The order and connection of ideas is the same as the order and connection of things.
Proof: This proposition is evident from Iax4. For the idea of everything that is caused depends on a knowledge of the cause, whereof it is an effect."

• This proposition is central to part II because it is the key to S's account of the mind/body relation.
• It is also very perplexing because for S, as for D, one can view ideas in two basic ways:
1. formally, they are mental occurrences whose psychological reality is that they are acts of belief.  Formally considered, an  idea is a mental episode whose cause is another mental episode.  This generates a psychological order of ideas.
2. objectively, they are the propositional contents of those beliefs, i.e., they are propositions.  Objectively considered, an idea  is a  proposition whose "cause" or logical ground is another proposition.  This generates a logical order of ideas.

NOTE: the psychological and the logical order of ideas need not coincide.  However, they seems to coincide (be appropriately isomorphic) when we reason correctly, that is, we have adequate ideas (Barbara example).
• From the uses S makes of IIp7, it is clear that it is supposed to apply both to ideas formally taken (mental events) and ideas    objectively taken  (propositions).
• IIp7 seems true if applied to true (adequate) ideas i.e., ideas in God's infinite intellect or in the human mind insofar as it has adequate ideas.  For then, the psychological order is the same as the logical order.  But the logical order of true propositions is the same as the order of the events they describe.
• However, things are much different if one considers ideas which are not adequate (true). For then, the psychological order is not the same as the logical order, and hence is not the same as the order of things.
• IIp7 has a very important note: a mode of extension and its corresponding mode of thought are "one and the same thing, expressed in two ways".

• It turns out that for S the mind is the idea of the body.
• The gist of the proof is that since man thinks (ax 2) and the idea is    prior to all modes of thought (ax 3), the basic element in the mind is an idea. But it cannot be the idea of a non-existing thing (it would not exist itself) or of an infinite thing (it would exist necessarily). Hence, it is the idea of a finite thing actually existing.
• In the corollary, S. explains that the mind is part of God's infinite intellect. Therefore, what humans perceive, God perceives, although not as absolutely infinite, but considered from the point of view of finite modes (modalized), i.e., constituting the essences of the various human minds.

• the proof is very obscure; it seems to have to do with the point that I alone am aware of my body in a special way.
• In the very important note, S does 3 things:
1. Claims to have clarified the mind/body relation.  In effect, mind and body are one thing.
2. Claims that the point just made can be extended to all things. This is equivalent to accepting panpsychism.

Problem:  Panpsychism is hard to accept without a theory of the unconscious or minute perceptions
3. Links the distinctness of ideas to bodily complexity.

C. The will, its alleged freedom and its relation to the understanding (props. 48-9)

The last two propositions of part II are devoted to a brief study of the will. S. concentrates on Descartes' theory of the will in Meditation IV and in the Principles: will as free and the cause of assent to propositions.
Prop. 48: there is no free, i.e., self-caused (self-initiating) will because the mind is a finite mode of God.
NOTE: In the note, S. claims that the same point can be made for any other mental operation, e.g., understanding, loving, desiring etc.  He takes this to show that there is no Faculty of will, understanding etc., but mere individual acts of volition, understanding etc.  Faculties are a product of the imagination, like Aristotelian natural kinds.
Prop. 49: "there is in the mind no volition, that is, affirmation or negation, except that which an idea, insofar as it is an idea, involves."

• The point here is that all acts of volition are acts of the understanding.  Hence, the will does not exist in two senses:
1. there is no faculty of will, but only individual volitions.
2. individual acts of volition are in reality mere acts of the understanding.

NOTES:
This entails an internalist theory of motivation
Eventually, in part III S. introduces a substitute for the will, namely, conscious conatus (endeavor)
• the proof is unclear.
• In the note, S. provides a long defense of his claim against some objections and then passes to consider some consequences of his view. Here we consider only 3 objections:
1. The will is infinite, the understanding is not, as Descartes holds.

Reply:  false, since we cannot will anything we cannot conceive.
2. We can suspend judgment and withhold assent from what we think. He who thinks of Pegasus needn't assent to its existence.

Reply: we don't have the power to suspend judgment. What seems willful suspension of judgment is nothing but  the realization that one does not adequately perceive the thing the judgment is about. The child imagining Pegasus without any other perception will assent to its existence.  Only by being aware that the idea of Pegasus is associated with another idea incompatible with it will make us deny or  doubt the existence of Pegasus.
3. If man has no absolute free will, then we're like Buridan's ass.

Reply: so what?
Problem:
S. seems right in criticizing Descartes, since belief seems independent of volition, at least of immediate volition.
However, he seems to go too far.  The rejection of the Cartesian position is compatible with the view that affirmation is a propositional attitude (a mode of thought) among others, although it has nothing to do with volition. One needn't go as far as S. and claim that ideas come to us as beliefs. The Pegasus example does not show that; it merely shows that imagining X brings about affirming X unless we are prevented from doing so by other images or knowledge we have.

D. Conclusion
If  S.'s enterprise is successful, the consequences are revolutionary:

• The traditional Western religions (Judaism, Christianity & Islam) are a pack of errors:
• God is not a person because, viewed as natura naturans, it has neither intellect nor will.
• The world has not been created by a benevolent deity, first because there is no creation, second, because moral attributes are human-bound.
• In place of the traditional concept of God, S. puts a scientifically inspired concept of Nature, viewed as a necessary, infinite, self-contained and intelligible system which operates in accordance with necessary laws.
• The human mind (the idea of the body) is removed from the special place it traditionally occupied (e.g., Descartes) and is fully integrated into Nature (full naturalism). It does not have mysterious powers over and above its activity.

Spinoza's political philosophy.

S's views are contained in two works, the Theological-Political Treatise (TPT) and the Political Treatise (PT) left unfinished at his death.  Both show Hobbes's influence.  Here we look mostly at two chapters of the former work, occasionally making use of material from the latter.  By and large, the political views espoused in these two works are the same, with one important exception involving the constitution of the commonwealth.

1.
God or nature, whose essence is power, is absolutely free.  Hence it has a right to all things; that is, God's right is coextensive with God's power.  But since there's no ontological inertia, individual modes (e.g., humans) exist only insofar as they embody divine power.  Hence, their right is also coextensive with their power.  In other words, might makes right (PT II, 3).  Hence:

• an individual has a natural right to pursue whatever end, irrational as it might be, by whatever means, maladjusted as they might be.  I
• since we are motivated only by the (subjective) perception of the good, one should keep a compact, agreement, or promise only in so far as one believes it's the best course of action available.

NOTES:
• S's view is more radical than Hobbes's, who had "merely" claimed that one has the right to employ whatever means (maladjusted as they might be) to pursue one's own survival.
• One may object that might doesn't make right any more than prudence makes duty; see, e.g., Rousseau's SC I. 3.

1. the TPT account: everyone resolves and contracts 1) to behave according to reason and bridle one's appetites.  However, in order to insure that such a compact is kept, everyone also agrees 2) to transfer one's rights to society as a whole in order to enforce the compact.  The result is a democracy.

NOTES:
• S. takes the state of nature to be historical (he says it's temporally prior to religion). Hence, presumably he takes the contract to be historical as well.
• The transition from state of nature to society is the result of the deliberate design of men acting rationally.
• Democracy, in contrast with monarchy and aristocracy is, for S, the best form of government.
2. The PT account: moved by their passions (e.g., fear and hope), men join forces, without a deliberate and rational design to improve their lives.  Moreover, no contract is mentioned (although S does allow that a people may transfer its right to a sovereign (TP IV,6)).

NOTE:
This account sits better with S's view in TP that men in the state of nature are barely rational (TP II, 15)

• to impose attitudes or acts which grate against human nature (e.g., to like what we deem disadvantageous and to dislike what we deem advantageous; not to be offended by insults; not to want to be free from fear, etc. (TTP XVII); to torture ourselves, to kill our parents; to testify against ourselves; to make no attempt to avoid death, etc. (TP III, 9).
• to impose laws which cannot be carried out (e.g., laws about how one ought to think or feel, or many laws enforcing morality)

• Since the sovereign cannot control men's thoughts, at most he can try to control speech.  But this favors mendacity, flattery, produces "martyrs," gives prominence to factions, etc., which are detrimental to the state, i.e., the power of the sovereign.
• Mere absence of war is a mere preconditions for citizens to exercise virtue, i.e. a life of reason, i.e., for S, a life of liberty.  For S, the end of society is liberty, and that is incompatible the people behaving like "puppets."
• That freedom of thought, speech and religious belief can be achieved without detriment for authority, S claims, can be seen from life in Amsterdam.

• speech which entails the nullification of the social compact (e.g., claiming that the sovereign has no  right, or various anarchist views) should be forbidden
• speech which invites sedition or civil disobedience (example of the man who disagrees with the law  and does more than 'reason' with the authorities in TTP XX) are to be forbidden.