I have a background in QFT, GR and differential geometry at the level of a master student in theoretical physics. I would like to touch the area of CFT. I know the textbook of Philippe Di Francesco. It may be too big for the beginner like me. Are there some good introductory lectures or textbooks adapted to the needs of beginners?
I would recommend the book Introduction to Conformal Field theory by Blumenhagen and Plauschinn. It is quite sort and can serve as a perfect introduction to CFT. It covers the basics of CFT in the first 3 chapters and then in the remaining 3 it goes on to introduce the CFT concepts that will appear most frequently in String theory.
I believe the content of the book was chosen with the beginning string theory phd student in mind, even though the phrase "string theory" rarely appears in the book. The style of writing is accessible to someone who is just beginning to learn about the subject and as far as I remember almost every statement in the book comes with a proof, which is quite refreshing for a physics oriented book.
The book is not complete in any sense and as you delve into the subject you will have to supplement it with other textbooks, like the Di Francesco, but it personally helped me learn the basics and not be completely lost in the CFT jargon during the beginning steps and I recommend it as an introductory book.