This booklet presents the key elements of graph theory, graph algorithms, and real-world applications of graphs simply and concisely. The intended audience is people wanting a basic introduction to the topic, one that covers a lot of ground but does not go into formal detail. The reader completely new to this topic will have learnt a lot about graphs by the time (s)he has finished reading this short booklet, just a handful of pages really.This booklet covers graphs of various types (undirected, directed, and weighted), defines key concepts (e.g., paths, cycles, matchings,cliques, isomorphism, …), states key theorems on graphs in plain-speak, defines fundamental computational algorithms on graphs, describes fundamental algorithms on graphs, and finally covers some important real-world applications.