This book is the founding document of phenomenology and the book (along with the works of Frege) which ultimately led to the analytic/Continental divide in philosophy. It is, therefore, a very important work not only in terms of understanding Husserl's own philosophy and the development of phenomenology but for anyone who is interested in the history of philosophy in the twentieth-century. It is a challenging work. Husserl's style is dense and somewhat dry and technical. You have to read very slowly and be prepared to re-read sections over and over but the result, if you have the patience, is very rewarding.
It is important to realize that Husserl's road to phenomenology began with the goal of grounding the objectivity of logic against the doctrines of psychologism (the doctrine that the laws of logic are based on empirical facts of psychology and are, therefore, relative to the species homo sapiens). The first section of this book is a really devastating critique of psychologism. This is important because phenomenology is often criticized for its subjectivism and its supposed lack of objectivity. Husserl's goal in this work is to ground the objectivity of logic against all forms of relativism (especially species relativism and the relativism that Husserl believes is inherent to Kant's philosophy).
Psychologism views logic as a technology of thinking, judging, proving, etc. and, therefore, believes it needs to investigate these phenomena, which are psychological phenomena, in order to work out a correct technology which would insure that we make correct or true judgements. Husserl writes, "Theoretically regarded, Logic therefore is related to psychology as part to whole. Its main aim is, in particular, to set up propositions of the form: Our intellectual activities must, either generally, or in specifically characterized circumstances, have such and such a form, such and such an arrangement, such and such combinations and no others, if the resultant judgments are to have the character of evidence, are to achieve knowledge in the pointed sense of the word" (33). This view seems to imply that this is a merely empirical question, namely: what form must our judgments take to possess the property of self-evidence and knowledge.
Husserl ultimately overcomes this view by distinguishing between the sense of an expression and the act of expression itself. The sense of an act of expression is ideal and is not a real part of the act in question (this is the distinction between noesis and noema). Logic, in Husserl's view, is not concerned with the acts of judging, thinking, proving, etc. but rather with the ideal laws relating to the sense of concepts like Truth, Proposition, Object, Property, Relation, Combination, Law, Fact, etc.; concepts which, in Husserl's own words, "represent the categories or constituents out of which science as such is essentially constituted" (51). Husserl points out that all forms of relativism which base themselves on the notion of a `subjective truth', or a truth that would be true for one person, or group of people, or one species, but not true for another, involve themselves in contradiction by using the word `truth' in a way that is contrary to its sense and meaning. According to Husserl, laws like the law of noncontradiction "have their roots in the mere meaning of truth, that from these it follows that talk of a subjective truth, that is one thing for one man and the opposite for another, must count as purest nonsense" (47). People who believe that it would be possible for there to be beings that would not be bound by logical principles like the law of noncontradiction (who believe that these are merely empirical facts about our own thinking) will either believe that such beings understand the words `true' and `false' in our sense, "in which case it is irrational to speak of logical principles not holding, since they pertain to the mere sense of these words as understood by us," or, "such beings use the words `true' and `false' in some different sense, and the whole dispute is then one of words" (48-49). In other words, anyone who uses the word "truth" and means the same thing that we mean when we use this word will be bound by the same logical laws as we are since logical laws relate to the sense of these words.
Logic is merely the expression of the laws relating to these ideal meanings. It is similar, in this way, to mathematics. Husserl points out that mathematics is grounded in acts of counting, addition, multiplication, etc. but no one views mathematics as being grounded in the psychological study of acts of counting, addition, and multiplication. Mathematics relates to the objects of such acts which are not real parts of the acts themselves. The same is true of logic in Husserl's opinion. While thinking is carried out in acts of judgement it does not follow that logic is based in the psychological study of such acts but rather in the ideal correlates of such acts.
Where Husserl differs from logicians like Frege is in his attempt to trace the ideal meanings of logic back to sense-bestowing acts of consciousness (though this is not a return to psychologism because we are not concerned with these acts in their empirical reality, or the causal mechanisms that give rise to them, but in their 'essence', i.e. in the aspects of these acts which would remain the same for any consciousness which was intentionally related to the same objects or meanings however different they may be from us in an empirical sense). "Phenomenology," Husserl writes, "lays bare the `sources' from which the basic concepts and ideal laws of pure logic `flow', and back to which they must once more be traced, so as to give them all the `clearness and distinctness' needed for an understanding...of pure logic" (86). In order to examine the sense of terms like Truth we must trace them back to the sense-giving acts which constitute them for consciousness though we will not be viewing these acts in their empirical reality as I have said (hence avoding psychologism) but will instead be viewing them in the pure generality of their essence. This leads Husserl to his notion of `eidetic phenomenology' in which the essences of various types of acts are grasped. The analysis of these acts reveals certain ideal possibilities and impossibilities in regard to the possible intuitive fulfillment of the intentional objects presented in these acts. These are certain ideal laws which apply a priori to our acts of intuition and signification (though the realm of signification is wider than the realm of intuition and is definied by purely logico-grammatical laws rather than laws of possible intuitive fulfillment which simply means that we can conceive things if they follow certain grammatical laws that could never be possible objects of intuition, i.e., a square circle).
The move back to phenomenology, and to consciousness, is ultimately what distinguishes Husserl from Frege and is what ultimately led to the Continental/analytic divide in philosophy. It is not enough, according to Husserl, to simply elucidate the ideal meanings relating to notions like truth; it is also necessary to inquire into how these meanings can be `given' to subjects or to consciousness. As Dan Zahavi writes in his book Husserl's Phenomenology (Cultural Memory in the Present), "If one wants to understand ideality, one ultimately has to return to the conscious acts in which it is given" (13). It is not enough for ideality, or the ideal laws of logic to exist, we have to know about them if we are going to talk about them at all. Zahavi again does a good job of summarizing this, he writes, "Even if it is impossible to reconcile scientific objectivity with a psychological foundation of logic, one is however still confronted with the apparent paradox that objective truths are known in subjective acts of knowing. And, as Husserl points out, this relation between the objective ideality and the subjective act has to be investigated and clarified if we wish to attain a more substantial understanding of the possibility of knowledge. We need to determine how the idealities are justified and validated by an epistemic agent" (11). This leads Husserl to his analysis of various acts and the modes of their intuitive fulfillment and leads him to a widened notion of intuition which includes what he calls `categorial intuition'. This was one of the most influential aspects of Husserl's early work and had a direct influence on Heidegger.
Husserl sums up his views fairly well towards the end of the work when he writes, "That a piece of sensory stuff can only be apprehended in certain forms, and bound together according to certain forms, that the possible transformation of these forms is subject to pure laws, in which the material element varies freely, that the meanings to be expressed are likewise limited to certain forms, which they can change only in prescribed manners, if they are not to lose their expressibility - all this does not depend on the empirical contingencies of the course of consciousness, not even on the contingencies of our intellectual or common-human organization. It depends on the specific nature of the acts in question, on their intentional and epistemic essence" (371). In other words, any intellect that can be intentionally related to a sensory object (to take one example) will be bound by the same laws that determine our own understanding in relation to such an object (and since the object and act are correlative one cannot change the act without changing the object). This means that even a divine intelligence would be bound by the same logical laws as we are (contra Kant).
In summary, this book is a really important book and is essential reading for anyone interested in Edmund Husserl, phenomenology, or the history of twentieth-century philosophy. Anyone who is critical of phenomenology should read this work; if nothing else it will illuminate the motivations that led Husserl to develop the method of phenomenology in the first place.