Coolant-Boiling in Rod Arrays -Two Fluids (COBRA-TF) is a thermal/hydraulic (T/H) simulation code designed for light-water reactor (LWR) vessel analysis. It uses a two-fluid, three-field (i.e., fluid film, fluid drops, and vapor) modeling approach. Both subchannel and 3D Cartesian forms of its governing equations are available for the solution. The code was originally developed by Pacific Northwest Laboratory in 1980 and has been used and modified by several institutions over the last few decades.COBRA-TF also found use at the Pennsylvania State University (PSU) by the Reactor Dynamics and Fuel Modeling Group (RDFMG) and has been improved, updated, and subsequently rebranded as CTF. CTF was later adopted in the early 2010s by Oak Ridge National Laboratory (ORNL) for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, which led to a significant advancement of the code's software quality, modeling accuracy, testing systems, and capabilities for improved support in modeling common LWR nominal and transient behavior. As part of the improvement process, it was necessary to generate sufficient documentation for the public domain code which had lacked such material upon being adopted by RDFMG. This document serves as a theory manual for CTF, detailing the many two-phase heat transfer, drag, and important accident scenario models contained in the code, as well as the numerical solution process utilized. Additional documents available in the CTF documentation suite include the user manual and the verification and validation manual.