Theory is what remains true when technology is changing. So, it is important to know and master the basic concepts and the theoretical tools that underlie the design of the systems we are using today and the systems we will use tomorrow. This means that, given a computing model, we need to know what can be done and what cannot be done in that model. Considering systems built on top of an asynchronous read/write shared memory prone to process crashes, this monograph presents and develops the fundamental notions that are universal constructions, consensus numbers, distributed recursivity, power of the BG simulation, and what can be done when one has to cope with process anonymity and/or memory anonymity. Numerous distributed algorithms are presented, the aim of which is being to help the reader better understand the power and the subtleties of the notions that are presented. In addition, the reader can appreciate the simplicity and beauty of some of these algorithms.