"Differential calculus on Normed Linear Banach Spaces" by Prof.Kalyan Mukherjee
This book gave me a very hands-on explorable window into the world of manifolds and Lie groups. Like it shows explicit calculations of derivative of matrix multiplication and determinant maps and also about computing tangents to curves inside Lie groups.
"Topology, Geometry and Gauge Fields" by Gregory Naber. (2 Volumes)
Its an exciting book which got me motivated into topology when it explained to me very simply the Heegard decomposition of S^3 and hence Hopf Fibration and how that relates to Dirac Monopoles! Before I read this book I had no clue that I would find mathematics exciting. Especially this revived my childhood interest in geometry.
Naber's are books that changed my career decision.
"Global Calculus" by S.Ramanan (in the AMS series)
This is a hard book to read initially but it excites the reader a lot and it was great to read alongside when Prof.Ramanan taught me topology and differential geometry. Anyway Prof.S.Ramanan is a great expositor. He could teach topics like modular forms and algebraic curves to a bunch of undergrads in their first complex analysis course in Chennai Mathematical Institute (CMI), India! He really pushes up the possible limits of exposition.
Prof.S.Ramanan's lectures in my alma mater CMI, affected my career choices almost as much as Naber's books did.
"Calculus on Manifolds" by Spivak
Its treatment of Fubini's theorem and related issues are great.
The writings on group theory by a college senior of mine called Vipul. His wiki "groupprops" is an amazing repository on finite group theory.
His extensive efforts into mathematical writing also inspired me into periodically LaTex-ing up interesting things in mathematics as I learn.
Can anyone here tell about nice expository writings on topics like Gromov-Witten theory or Reshetkhin-Turaev and Rozansky-Khovanov stuff and how these relate to QFT? Something which shows a lot of examples and may be also explicit calculations.
Most sources on Quantum Groups that I have tried looking at start off a bit harshly for the newcomer. I would be greatly interested to read of "great mathematical writing" in these areas.