Exploring Formalisation : A Primer in Human Readable Mathematics in Lean 3 with Examples from Simplicial Topology Introduction 1 The Lean Proof Assistant 2 Basic Examples 3 Design Choices 4 Abstraction and Prototyping. This primer on mathematics formalisation provides a rapid hands on introduction to proof verification in Lean. After a quick introduction to Lean the basic techniques of human readable formalisation are introduced illustrated by simple examples on maps induction and real numbers. Subsequently typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher dimensional generalisation of graph theory). Finally the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers. Informed by the authors recent teaching and research experience this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter familiarity with elementary category theory and algebraic topology is recommended.