The software development process developed largely by the Three Amigos (Ivar Jacobson, Grady Booch and Jim Rumbaugh) through their collaborative work at Rational Company.
The cornerstones of the process are that it is:
Use-case driven
Architecture-centric
Iterative and incremental
The Rational Unified Process is the implemented and branded version of this, with fancy tools and the rest.
The process consists of four main phases: inception, elaboration, construction and transition. Each of these contains one or more iterations across five core workflows: requirements, analysis, design, implementation and test. (RUP adds other flows like project management, documentation etc.).
The Usdp Book describes the process in lots of detail, down to roles, activities and artifacts in each phase and iteration. It it however intended to only be an abstract process. Any process implementation (such as RUP) will only use whichever bits are needed, and add whatever else is required.
See original on c2.com 