Abstract Algebra book with exercise solutions recommendations.
A simple search on Google shows the following:
Abstract Algebra Manual ( Problems and Solutions ) by Ayman Badawi
http://www.math.niu.edu/~beachy/abstract_algebra/review/review.pdf
http://shell.cas.usf.edu/~wclark/Elem_abs_alg.pdf
https://www.dpmms.cam.ac.uk/~oh233/old/algebra1/book.pdf
Schaum's Theory & Problems of Abstract Algebra by Joong Fang
Gallian's book has selected exercises' solutions (apparently all the odd numbered ones)
Weiss's "First Course in Algebra and Number Theory" has lots of solutions
Whitesitt's "Principles of Modern Algebra" has many solutions
Krechmar's "A Problem Book in Algebra" (high school level) has all the solutions
Vinberg's "A Course in Algebra" has some solutions
Faddeev-Sominskii's "Problems in Higher Algebra" (high school-basic linear algebra) is all solutions
Gilbert's "Elements of Modern Algebra" has many solutions.
Etc.