Pinter, "A Book of Abstract Algebra", is very nice. It's rigorous but not too terse. It divides the material into many small chapters with many exercises. Chapters are mostly around 10+/-3 pages with about 40-60% of that being text and the rest exercises.

The exercises for each chapter are split into several sections each section covering a different aspect of the chapter's material. Sometimes there is a section of exercises applying the material to some interesting area.

For example, the chapter on groups of permutations has 6 pages of text, then 5 pages of exercises divided into 9 sections. Those sections are: computing elements in S6 (5 problems), examples of groups of permutations (4 problems), groups of permutations in R (4 problems), a cyclic group of permutations (4 problems), a subgroup of SR (4 problems), symmetries of geometric figures (4 problems), symmetries of polynomials (4 problems), properties of permutations of a set A (4 problems), and algebra of kinship structures which consists of 9 problems covering how anthropologists have applied groups of permutations to describe kinship systems in primitive societies.

There are answers in the back for a decent number of the exercises.

It's a Dover republication so is not too hard on the wallet. List price is $30 at Dover but its around $20 on Amazon.

The combination of short chapters and lots of exercises make it easier than most textbooks to fit into a busy adult schedule.

Abstract Algebra: A Student Friendly Approach by Dos Reis and Dos Reis [0] is like The Little Schemer but if it was a first course in abstract algebra.

[0] https://www.amazon.com/gp/product/1539436071?psc=1

I assume you're talking about an algebra book for self-study? Gallian's "Contemporary Abstract Algebra" is a common suggestion for a more accessible algebra book, and people also sometimes suggest Fraleigh's "A First Course in Abstract Algebra", but I can really only speak to what it's like to work on this stuff with a teacher --- since my students are by definition not self-studying the things I'm working on with them, my suggestions might be of limited use!

In general, I think self-studying proof-based math can certainly be done if someone's motivated enough, but it's pretty hard and takes a lot of work, especially if you're still getting used to the skill of reading and writing proofs. It's very valuable to be able to have a person available to evaluate the proofs you're writing, and I've definitely seen a few people who came to me thinking they'd mastered proof-writing on their own and were kind of mistaken about that. (I've definitely also seen people who really did learn this skill pretty well without help! It varies a lot.)