• One, pretty mathy, but classic book about Riemannain manifolds is: Semi-Riemannian Geometry by O'Neill.

• Some approachable Lie Algebra notes are available here, they are designed to require little background: Lecture Notes on Lie Algebra.

• My personal favorite book about Algebraic/Differential Topology is : Calculus to Cohomology. This book is extremely approachable, requiring only multivariable calculus and linear algebra to completely understand it. I cannot recommend it enough, particularly for physics.

Also I third Road to Reality. It is a very fun/interesting book!