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I’m not looking for resources that explain tosafot’s commentary , rather that which explains tosafot’s dialectic, syntax and other components utilized in tosafot’s commentary.

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This is a good book for a beginner and also for last. Learning tosfot is really learning talmud. All the mefarshim, rishonim and acharonim address the limud of tosfot. In yeshivot people say that if you don't understand the Maharsha, this is a proof that you didn't read accurately the tosfot. So Maharsha (called chidushe halachot) is the main relevant book on tosfot for most people, with Maharshal and Maharam. Mahari Ben Lev, and Torat Chayim, that are not printed in the Vilnius Talmud édition but are in the same category of basics for tosfot learning. But if you are still beginning and learn alone, the first (Chidushe Hatosfot) that you can see in the link can help you a lot to learn tosfot, this book helps to decifer the structure.

In tosfot you need first to translate the text in "formal language", kushia, teruts, reaya, stira. Several times the structure is implicit, tosfot anticipate that he will refute an explanation before its explanation. You must translate "this is an explanation", but it's not agreed because x and y reason. And later tosfot quoted a rav that defends this opinion. If tosfot rejected a guirsa, you need first explore the pshat of the talmud with this girsa, or if he rejected the Rashi commentary, you need to explore it first. Each of the pshatim has strong points and weak points, tosfot makes comparison between them. The text of tosfot is very concise and you need to make your own length paraphrase with all details addressed. It's help to see e.g. Tosfot Harosh or Tosfot Santz, Tosfot Rabeinu Perets that are lengthened versions of tosfot help to decifer the tosfot on the daf which is a shortened version.

Ve im Tomar comes as a consequence of the text above. Vechi tema Is a refuted teruts. Mihu, Ela is a refutation, af Al gav is a refuted objection. Veod yesh lomar is a new teruts because of a dochak in the first "Veein lehakshot de..." is a kushia followed by a teruts. You can learn darkei hatalmud from Rabbi ytschak kampenton to help the tosfot learning. Finally tosfot is very structured and the important is to find the words that work as "operators".

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