The renormalization group (RG) method has found applications in many areas of physics. The authors present simple RG treatments of such diverse problems as random walks, percolation, chaos and critical phenomena. Detailed introductory materials are presented in each area which makes it reasonably self-contained. The concepts of self-similarity and scale invariance are a common thread tying these problems together. Emphasis is placed on intuitive real-space RG calculations rather than formalism. The momentum-space RG is introduced and the 1/n and epsis expansions are discussed. A brief explanation of the field-theoretic approach to the RG serves as an introduction to more advanced techniques.