Group theory doesn't ask you to learn a new kind of mathematics so much as a new way of looking at mathematics you already have. Every tool this chapter reviews was built in Discrete Mathematics I for a different job, and every one of them gets reused here for a job it was never advertised for.
A set stops being just a bag of numbers and becomes a bag of anything that can be combined -- integers, remainders, rotations, functions, matrices. A function stops being just a graph and becomes the exact lens for comparing two algebraic structures: Chapter 2's isomorphisms are nothing but functions with an extra promise about how they interact with an operation. An equivalence relation stops being an abstract exercise in reflexive/symmetric/transitive and becomes the machinery behind cosets, the partition a subgroup cuts a group into -- the single idea Lagrange's theorem is built on. Induction stops being a proof template for sums and becomes the standard way to reason about every power of a group element or every step of an algorithm on a group. And divisibility and gcd stop being number-theory trivia and become the reason \mathbb{Z}_n has exactly \varphi(n) generators -- a fact Chapter 3 leans on directly.
None of the six sections ahead teach a new technique. Each one takes a tool you can already use on numbers and asks you to notice what made it work in the first place, so that when Chapter 1 asks the same question about a rotation, a permutation, or a matrix instead of a number, the answer transfers without having to be relearned. If a definition here feels unfamiliar, the fix is a trip back to the relevant Discrete Mathematics I section, not a new idea to absorb -- everything in this chapter is exactly as it was taught there, only pointed in a new direction.
By the end of this readiness review, the vocabulary of sets, functions, equivalence relations, proof, induction, and divisibility should feel like a shared, reliable language rather than six separate topics -- because starting in Chapter 1, group theory is going to speak in that language constantly, and rarely pause to translate.