  This chapter is divided into two parts. The first is largely expository and
builds on Karandikar's axiomatisation of It{\^o} calculus for matrix-valued
semimartin-gales. Its aim is to unfold in detail the algebraic structures
implied for iterated It{\^o} and Stratonovich integrals. These constructions
generalise the classical rules of Chen calculus for deterministic scalar-valued
iterated integrals. The second part develops the stochastic analog of what is
commonly called chronological calculus in control theory. We obtain in
particular a pre-Lie Magnus formula for the logarithm of the It{\^o} stochastic
exponential of matrix-valued semimartingales.
