Contents 1 Introduction and motivation: physical phase transitions 2 2 Mathematical abstraction: macroscopic order from microscopic disorder 4 3 The Thermodynamic Formalism and lattice gases 7 3. 5 Bond percolation 22 6 The Ising ferromagnet and bond percolation in two dimensions, and Peierls' argument 23 7 Other important ideas 28 7. Prerequisites This essay covers a number of different mathem...