Sicilian Defence (1. e4 c5) and how to develop it further by using different variations. It is easy to learn, it has hundreds of years of history and it is very popular in grandmaster tournaments.
I think the most common thing to implement is the perceptron algorithm from scratch.
I would recommend Pattern Recognition and Machine Learning by Christopher M. Bishop. It assumes no previous knowledge of pattern recognition or machine learning.
Learn You a Haskell for Great Good! is aimed at people who have experience in imperative programming languages but haven't programmed in a functional language before.
Esoteric programming languages are usually created to bend the boundaries of programming language design or prove something, not to be actually used to write software. It is hacker culture.