The equation ax = bx + c

Planar nearrings are nearrings with the property that it solves equations ax = bx + c whenever there is some u such that au and bu are different. They are proven to be rich in applications, in other mathematics areas and beyond. This book provides an introduction to the subject and its connections to combinatorics and geometry. Starting from nine problems, ideas are formed and different combinatorial and geometrical objects are defined. These problems are solved when various properties of planar nearrings are developed. The book will be suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a clear and elementary manner. Appendix provides some background material on basic algebra.