This e-book is the Basics Edition. It illustrates the common, and essential data structures algorithms underscoring the BIG O Time Complexity basics. It also details, with examples, using one of the world's most commonly used web server-side programming language (PHP) to describe how it can be applied or implemented by developers, and novices alike, for the real-life scenario solutions. It includes highly valued examples, test code, run and test outputs, and several useful reference points.The objective is to help, established software developers, up-coming developers, scientists, mathematicians, and software novices alike. It captures the common, and the essential basics of data structures algorithms of the BIG O Time Complexity, and described them in clear, and unambiguous terms, detailing where and how to apply them in solution development in the real world. It includes great examples code, test code, runs and test outputs, written with PHP under apache server and MySQL server. Note: PHP is a web server-side programming language. The aim is also to make it, serve as a first-hand personal reference guide, for anyone that may need it, or have to tackle solution/s involving, the Time Complexity with data structure algorithms, but also software developers/programmers, scientists, mathematicians, who may have at one point in their solution designing, and implementation work-life, encountered the Time Complexity scenarios. This e-book provides a comprehensive basic list, and addresses, the down-to-basics, of how to handle, and implement the time complexity issues, and how to turn them into viable implementable real-world solutions.