Introduction
What does it mean to learn Gemara B'Iyun and why would I want to?
The stereotypical definition of learning Gemara B'Iyun relies on the number of מפרשים that you consult. If you open many books and read many explanations of the Gemara then you are learning the Gemara in depth.
However, this is an insufficient description. You can read many explanations on a surface level without gaining a more conceptual understanding of the Gemara than you would have had otherwise.
Iyyun learning requires conceptualizing the textual information you are studying. Conceptualizing means abstracting or generalizing underlying principles from the case you have just studied.
Iyyun learning is based on bekiut, textual analysis. We will give you tools for doing both kinds of learning
In order to define what learning Gemara B'Iyun means (and how to do it) we first need to introduce the concept of חידוש.
The working assumption when approaching the Talmud as a legal text is that every halachik statement is presented for a reason. While there are exceptions to the rule in a small minority of cases, for the vast majority of cases this is going to be the case. Thus, for every halachik statement we can pose the question: Why was this halachik statement brought? What does it contribute to my understanding of the issue that I would not have known otherwise? Or in other terminology: What is the חידוש of this halachik statement? What is its precedent value?
You can view the חידוש in a localized context - without the ruling presented in response to a particular case we would not have known what the דין should be (in that case). The assumption when learning Gemara B'Iyun is that the ruling presented represents a rule that can be applied in more cases than the specific one presented in the text. The Gemara presents us with a case which is meant to instantiate an underlying legal rule which is the basis for the ruling in the given case. (In more legal terminology - We may then say that the statutory law is presented as case law.)
Thus, the first goal for the person learning Gemara B'Iyun is to determine the rule embodied in the case being analyzed. Once the generalized rule is articulated, it may be applied to adjudicate cases not mentioned in the Gemara. The ability to analyze a Gemara text so that the student can "tease" out the rules governing not just the case at hand but all others which may be governed by this rule, is at the heart of learning b'iyyun.
Subsequently analyzing multiple related cases will allow us to build up an overall framework to address an entire area of Halacha. Relating areas and creating larger frameworks will allow the student to create a full framework of all areas of Halacha. This is what חז"ל have done with ששה סדרי משנה, the רמב"ם provided an alternate framework in his יד החזקה and the טור (followed by the שולחן ערוך) did for a subset of Halacha in the ארבעה טורים.
The goal of this project is to present a systematic set of tools that will allow anyone to acquire the skills to understand and participate in the discussion. Ultimately, they should be able to create their personal halachik framework as their expression of תורת הקב"ה.
Why learn biyyun?
First, it gives both a deeper, and therefore a broader, more encompassing understanding.
Deeper, because the conceptualization/abstraction reveals the more fundamental halakhic principles generating the specific case you've studied on the bekiut, textual level. In and of itself, this is a halachically desirable intellectual activity. But it has practical consequences as well because it gives us a more encompassing understanding, because armed with the conceptual principles which generate the specific case, you can apply them to other specific case hitherto not discussed You can adjudicate new and variant cases.
Indeed, this is one of the reasons the Torah itself encourages Torah study [cite source].
You see, neither the Torah nor, lehavdil, any other law system can a priori account for all possible cases that can arise in real life. Thus the Torah shebichtav provides us with some ideal case - ideal in the sense of it encompassing all the variables necessary for ruling properly and for a perfect fulfillment of the halachic requirement. It then assigns to Torah shebal peh - us included! - the task of working out of the rulings in less than optimal cases.
For example, an ideal shechita includes the person who is ideally suited for doing the shechita - someone who is of legal age, pious, knowledgeable in the law, with the necessary physical dexterity and previous experience doing shechita.
What however is the ruling in a case where a less than ideal shochet performs the shechita?
For example, what if the shochet is a child, an apostate, a non-Jew, is handicapped etc.?
Adjuticating that case requires that we understand which of the ideal variables for choosing a shochet are necessary and which are at best, just desirable.
Or, if the ideal fulfillment of sippur yetziat mitzraim involves a father teaching his son, what is the ruling for someone who will be isolated from his family on Pesach night?
A final word on how this project has been developed. Our goal is to present a model of what every competent Talmudic scholar must be doing in order to excel at learning in the ways he does. We constantly asked what mental processes must be involved in order for the student and master of Gemara learning to succeed in his learning. From the answers we have found. we have created a number of templates of information gathering questions and clearcut guides for answering them, and a (reasonably flexible) sequential program for asking and answering them, such that if followed, will allow you to recognize and replicate to greater and lesser extents, the kinds of learning-analyses that typify the masters.