Background required to understand the mathematical definition of knots and their transformations

Question

What are the concepts of math required as a prerequisite to understand Knot Theory?

I'd like to be able to make a humble beginning by being able to mathematically define knots and the non-rigid transformations one can make with knots made of ropes, in real life.

Answer 1

You don't need to have an extensive background to understand the fundamental ideas of Knot Theory. I would suggest reading The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots by Colin C. Adams. It's an excellent introduction to the subject and it will give you a starting point for further studies.

From the Preface:

My hope is that this book will excite people about mathematics--that it will motivate them to continue to explore other related areas of mathematics and to proceed to such topics as topology, algebra, differential geometry, and algebraic topology.