
1. Journey into Mathematics by Rotman
2. Street Fighting Mathematics by Sanjoy Mahajan
Journey into Mathematics: An Introduction to Proofs (Dover Books on Mathematics) https://a.co/d/csM8jRd
I seem to remember that by design it didn't require any advanced maths to get started constructing proofs. Good luck!
1. The foundations of mathematics by Stewart and Tall
2. Problem Solving Strategies by Arthur Engels
3. Journey into Mathematics by Rotman
4. Concrete Mathematics by Knuth et al.