Suggested General Reference
Principles of Condensed Matter Physics, by P. M. Chaikin & Tom Lubensky, is an excellent resource for learning soft matter physics.
It is a clear, surprisingly self-contained exposition to advanced topics in statistical physics and their applications, as well as dynamical critical phenomena, hydrodynamics, topological defects, and interface phenomena (e.g. the 'roughening transition' for solid-fluid interfaces). This is a graduate level book.
Additional general references (mainly statistical mechanics)
Entropy, Order Parameters, and Complexity, by James Sethna, is highly readable, contains many thoughtful exercises, and is free on the author's website.
Phase transitions and Renormalization Group, by Jean Zinn-Justin, gives a more concise, mathematical treatment of renormalization group methods, as well as the canonical topics of statistical field theory. This book also has many instructive examples.
Statistical Mechanics of Phase Transitions, by J. M. Yeomans, is short, but gives a great conceptual overview of theoretical techniques in the analysis of phase transitions.
The statistical mechanics textbooks by Mehran Kardar (Statistical Physics of Particles/Fields) are phenomenal. The second volume gives a comprehensive treatment of field theoretical methods, and has a nice chapter on directed polymers in random media and stochastic growth models. Both books include many interesting problems.
Polymer physics
Introduction to Path Integral Methods in Physics and Polymer Science, by F. W. Wiegel.
An introduction to standard models of polymers, and path integral methods more generally. Very well written, (but lacks exercises).
Scaling Concepts in Polymer Physics, by P. G. De Gennes,
Introduction to Polymer Dynamics, also by De Gennes.
Best Answer
I really enjoyed
though to be honest it's now getting uncomfortably close to fifteen years since I read it as a high school student, and I don't have my copy at hand to give it a critical assessment. As a high schooler I found it engaging and accessible, and if you want to you could see it as very successful in my case - it was my first introduction to quantum paths, and here I am working in the field a decade later, though I'm unsure that effect is uniform across its readership. As I recall, though, I looked it over a few years ago and didn't find anything that was worryingly inaccurate or misreepresentative of how modern quantum physicists see the field.