Here I would like to briefly address Transcendental Apperception. This is by no means an exhaustive treatment, but potentially helpful for matters of interpretation.
(This post is adapted from some of my comments in reply to a discussion concerning a criticism Whitehead had of Kant.)
Transcendental Apperception and Transcendental Subject:
A criticism of Kant is that the human subject still remains privileged even after the Critical Turn. This would leave Kant firmly in the tradition of the reading of other Modern period thinkers (Descartes, Hume, &c) who maintain the radical dualistic subject-object relationship so frequently criticized by contemporaries (I think that these Modern thinkers are accused of a mistake they do not make entirely, but I will leave that for another time and place). I do not find that this is an accurate account of Kant, and hopefully I can clarify this by clarifying the distinction between 'Transcendental Subject' and the 'Transcendental (Unity of) Apperception' which is first developed in the Transcendental Deduction of the Critique of Pure Reason.
It is important to see what is at stake when the Transcendental Apperception is developed - this is what the concern is:
"If we were not conscious that what we think is the same as what we thought a moment before, all reproduction in the series of representations would be useless." (CPR A103)
Here is an example of what Kant means: If a ball is thrown and I am to catch it, I must be able to track the ball, and the ball must remain a unity (unitary ball) over different representations (of balls). While the representations must be distinct, it is due to a different power that the representations (of the ball) are thought as a unitary ball. This unitary ball is distinct from the separate representations, but because it is not a representation it is not known in any distinct way save for as an object in general. (An object in general is an object free from all empirical conditions.)
Given any number of consciousnesses which feature a representation of the ball we are conscious of a distinct ball, but these will not yet allow for the sort of interaction with the ball wherein we can track the ball as one thing and catch it over the course of a duration of experience; for this we need more than the separate representations, but their ordered relation as a unitary ball. This unitary ball we experience is an object in general thought in conjunction with the representations of balls in consciousness. This is the Transcendental (Unity of) Apperception at work.
To get a bit more precise: if any representations are to be able to be thought as exhibiting any rule in experience (even a false rule), then these representations need to be conformable to rule giving, which means that the representations must be able to be thought in a unity, or as relating to one thing (an object in general).
In important distinction from this, the Transcendental Subject is the object in general thought as the unity of all experience generally. That is, it is an obvious rule that all we experience is experienced. This rule is only able to be exhibited in experience, and the possibility of exhibiting this rule rests on Transcendental Apperception.
This Transcendental Subject itself is only possible through Transcendental Apperception, and so is not privileged any more than the objects of our experience (balls, etc) as concerns rules. What makes the Transcendental Subject different from empirical objects is that we do not necessarily think any particular empirical object, let alone any rules for them, but insofar as we are experiencing we think the Transcendental Subject.
The Importance of Transcendental Apperception in the Transcendental Deduction:
The Transcendental Deduction is renowned (unfortunately) for being very difficult. Transcendental Apperception is a step in the deduction that is very important, and since the subject is broached and explained above, it may help to give the importance of this step to the Deduction generally.
The concern that leads us to require Transcendental Apperception is the question concerning putting objects to rules generally. If we did not relate all representations to each other there would be no law giving in relation to those representations. The Transcendental Apperception serves the role, and only the role, of unifying experience in this most fundamental way such that thoughts of objects can occur in the form of rules. The Transcendental Apperception must take an object to stand for the otherwise disparate representations, and this unitary object is an 'object in general' because this object is never given itself in any of the representations.
When we recognize that an 'object in general' is necessary for the connection of our representations into experiences that obey any sort of rule, then we find that we must account for this object in general through a priori means, and cannot derive it from experience, since experience is incoherent (without the possibility of rule) without it. The possibility of thinking an object in general in the various ways we do is given by the categories. It is the objective of the Transcendental Deduction to give the necessity of the Categories.
Hopefully this demystifies the Transcendental Deduction a bit.
Additional Matters of Consideration:
In the Norman Kemp Smith translation of the Critique, it may be important to clarify the terms 'mind', 'consciousness' and 'representation'. I will try to give a brief account of how I am thinking of these right now.
Mind seems to be the 'place' where thoughts 'happen'. This place and happening are thought but cannot be given within any experience, and so are transcendental.
Consciousness is the totality of representations at any time.
A Representation is something that we are conscious of which can be thought in relation to an object in general.