For precalculus see here. What exactly is "Algebra II"? Serge Lang has "Algebra" (I suppose I, II, and III).

What I mean by algebra II here is polynomials, quadratic equations, matrices, logarithmic and exponential functions, inequalities, and maybe an introduction to sets. Also, you can suggest multiple books on different topics instead of one big book titled precalculus. Also, please suggest books on trigonometry

I am aware of that question Dietrich Burde but I want a more modern treatment of the subjects. Also by algebra, I do not mean abstract algebra.

What level are you aiming at? Do you want an elementary treatment of these topics, or would you be comfortable with a textbook that would eventually introduce you to abstract algebra, e.g. groups, rings, fields, Galois theory etc?

An elementary treatment of these subjects as I am only in high school.

Check out Serge Lang's Basic Mathematics. Lots of discussion on various forums.

I already have that one. It is good but does it does not cover trigonometry and some other topics in a very comprehensive way.

*but it does not

Algebra 2 generally means domain, range, basic trig, functions, polynomials, inductive reasoning, inequalities.

One of the problems in books at this level I've found is that the more advanced/honors types fall into two essentially non-overlapping categories: (1) great attention to logical formalism and notation; (2) lots of nontrivial results and problems. Books of type (1) tend to be mathematically simple once you get accustomed to the (in my opinion) over emphasis on mathematical formalism, and books of type (2) tend to go out of their way (or were written too long ago) in avoiding getting you familiar with modern formalism. (continued)

An example of type (1) is The Non-Algebraic Elementary Functions: a Rigorous Approach by Andre L. Yandl (review), and examples of type (2) can be found here and my comments here.

Books that might work for you: Elementary and Advanced Trigonometry by Kenneth Sielke Miller and John Breffni Walsh AND Modern Introductory Analysis by Mary P. Dolciani AND Fundamentals for Advanced Mathematics by Abraham M. Glicksman and Harry D. Ruderman (not well known, but should be) AND these School Mathematics Study Group texts.

I notice that the School Mathematics Study Group link I gave omits some of the more advanced titles, such as this book on matrices for high school students. I posted a list of several of the more advanced titles somewhere, but I've been unable to find it. This might be one of my answers in Stack Exchange that has disappeared due to the person who asked the question deleting their question. (I know it was an answer, not a comment, and thus if it still exists it should come up with an appropriate google search, but it hasn't.)

Thank you for your suggestions, David L. Renfro. I can accept suggestions for a less rigorous textbook as well if it is comprehensive and thorough in its explanations.

Also, can anyone suggest a geometry book as well if possible?

Why has my question been closed? I think this question has enough specifics to be focused and to encourage minimal discussion. The feedback given to me does not give a satisfactory explanation for closing my question. I have done the edits that I think will improve the clarity of the question and added a tag that I thought was necessary.

Please, avoid making several edits.