1: For some proofs with good visual input are (I think this are the books that most agree with the question asked, in fact some demonstrations have almost only drawings.) : Proofs without Words I, II and III, R. B. Nelsen .
2: If you want to know a little groups more quickly, one of my favorites is: Visual Group Theory,N. Carter.
3: To know some of the concepts of number theory it can be interesting to see: An Illustrated Theory of Numbers, M. H. Weissman. Nuggets of Number Theory: A Visual Approach, R. B. Nelsen.
4: If the mathematical logic is of your interest, i.e. the reasoning of the arguments with diagrams. A good choice to read:
Visual Reasoning with Diagrams, A. Moktefi, S. Shin (Editors).
5: The complex analysis has always had a visual version, some good ideas can be seen in:
Visual Complex Analysis, T. Needham. Visual Complex Functions: An Introduction with Phase Portraits, E. Wegert.
6: If the topic of interest are the most abstract themes of differential forms and varieties, My recommendation is to see this book: A Visual Introduction to Differential Forms and Calculus on Manifolds. J. P. Fortney.
7: For those who have an interest in graph theory, the combination with algorithms and drawing the graph can be interesting. Graph Drawing: Algorithms for the Visualization of Graphs, I. G. Tollis, G. Di Battista, P. Eades, R. Tamassia (Authors).
8: Beautiful Evidence, E. Tufte: some photos help explain concepts.
9: From numbers, trigonometric functions, geometry, transformations that preserve area, and much more: Math Made Visual, C. Alsina and R. Nelsen.
Some other references can be found in the following link, mainly topology books.