TBLIS is a library and framework for performing tensor operations, especially tensor contraction, using native algorithms. In this context, native means that TBLIS does not translate tensor operations into matrix operations using the BLAS libraries. Instead, TBLIS uses the philosophy (and certain low-level kernels) of the BLIS framework to implement tensor contraction with essentially zero overhead compared to matrix multiplication. TBLIS also aims to offer a convenient C++ interface for tensors and tensor operations, as well as a stable C interface with high portability.