  We discuss the polarised fragmentation functions of quarks and gluons in
Perturbative Quantum Chromodynamics. The Altarelli-Parisi evolution equations
governing these fragmentation functions are presented. We find that the first
moment of the polarised gluon fragmentation function to order $\alpha_s$ is as
important as that of the quark and anti-quark fragmentation functions. The
$\Lambda$ production in polarised $e^+ e^-$ annihilation where this can be
realised is discussed. We propose the factorisation method to compute the
gluonic contribution to $\Lambda$ production to order $\alpha_s$. With
appropriate operator definitions for the quark and the gluon fragmentation
functions, we find that the hard part of the factorisation formula is free of
any infrared singularities confirming the factorisation.
