  Motivated by the bootstrap percolation process for graphs, we define a new,
high-order generalisation to $k$-uniform hypergraphs, in which we infect
$j$-sets of vertices for some integer $1\le j \le k-1$. We investigate the
smallest possible size of an initially infected set which ultimately percolates
and determine the exact size in almost all cases of $k$ and $j$.
