  This is a system paper about a new GPLv2 open source C library GBLA
implementing and improving the idea of Faug\`ere and Lachartre (GB reduction).
We further exploit underlying structures in matrices generated during Gr\"obner
basis computations in algorithms like F4 or F5 taking advantage of block
patterns by using a special data structure called multilines. Moreover, we
discuss a new order of operations for the reduction process. In various
different experimental results we show that GBLA performs better than GB
reduction or Magma in sequential computations (up to 40% faster) and scales
much better than GB reduction for a higher number of cores: On 32 cores we
reach a scaling of up to 26. GBLA is up to 7 times faster than GB reduction.
Further, we compare different parallel schedulers GBLA can be used with. We
also developed a new advanced storage format that exploits the fact that our
matrices are coming from Gr\"obner basis computations, shrinking storage by a
factor of up to 4. A huge database of our matrices is freely available with
GBLA.
