These notes are associated with the software release of T-IFISS. This is a suite of m-files for solving steady diffusion problems in a general two-dimensional geometry using the finite element method. Unstructured mesh generation is effected using the DISTMESH package. The T-IFISS package has five main ingredients: o Discretisation with linear (P1) and quadratic (P2) elements o Visualisation of the computed solution o Built-in a posteriori error estimation of the generated solution. o Self-adaptive solution driven by rigorous energy error estimation o Iterative solvers can be tested on the resulting linear systems Major changes/additions in version 1.2: . choice of three types of error estimation strategies using piecewise linear bubble functions for P1 approximations (element residual (default), global hierarchical, 2-level) . choice of edge- or element-based marking (for hierarchical and 2-level error estimation) . goal-oriented adaptivity with 6 different marking strategies . fast (vectorized) mesh refinement