Question

What are good textbooks to cover these topics?

Sets: sets and their elements, finite and infinite sets, operations on sets (unions, intersections and complements), relations between sets(inclusion, equivalence), non equivalent infinite sets, cardinal numbers.

Binary Operations: basic definitions, associativity commutativity, neutral elements, inverse elements, groups.

Functions: introduction, Cartesian products, functions as subsets of Cartesian products, graphs, composition of functions, injective, bijective and surjective functions, invertible functions, arithmetic operations on real functions, groups of functions.

Plane isometries: definition, reflections, translations and rotations, compositions of reflections, congruent triangles and isometry, classification of the plane isometries, the group of plane isometries, applications in Euclidean geometry.

Axiom systems: undefined terms, axioms and theorems of axiomatic mathematical theories, models, consistency, independence, completeness and categoricity of axiom systems, finite affine geometries.

Euclidean geometry: historical notes, a modern representation of Euclidean plane geometry as an axiomatic theory. The natural numbers: an introduction to peano's axioms,arithmetic operations, order relations, first steps in number theory, mathematical induction.

Answer 1

​ The best books to study the given topics are follows

Sets : ​if you want to have a good and brief knowledge abouts sets, then best book is ​Mathematics (IX) by RD Sharma (Indian author). this book has a chapter on sets. ​if you want to study in depth about sets you can follow ​Naive set theory by Paul halmos.

​Binary : ​for binary operations there is no special book on binary but you can follow Digital Electronics by Prof. S.Salivahan.

Functions : ​for functions also if you want to get brief and good knowledge you can follow ​Mathematics (IX) by RD Sharma (Indian author). ​this book also contain a special chapter on functions only. and for more you can follow ​NCERT Mathematics class IX ​for good question practice.

Plane isometries: ​for this section you can follows you can follow Piping Isometrics.

Axiom systems: ​for this section you can follow axiom(TM): The Scientific Computation System by Richard D. Jenks​. you can aslo follow The Axiom System of Book I of Euclid's Elements of Geometry ​by Dr. David R. Wilkins

Euclidean geometry: ​there are many books on Euclidean geometry but the best rated book is Advanced Euclidean Geometry (Dover Books on Mathematics) by Roger A. Johnson​. you can also follow Euclidean and Non-Euclidean Geometries: Development and History by Marvin J. Greenberg.