Chapter 1 of 'Java Software Solutions: Foundations of Program Design' covers the fundamentals of computer systems including hardware and software components, programming, and computer networks. It delves into the architecture of the CPU, memory types, and the binary number system, while also discussing the importance of the Java programming language and object-oriented software development principles. Additionally, it outlines the problem-solving process in programming, addressing how to develop effective solutions and the associated program structure in Java.