  In this work, we introduce Regularity Structures B-series which are used for
describing solutions of singular stochastic partial differential equations
(SPDEs). We define composition and substitutions of these B-series and as in
the context of B-series for ordinary differential equations, these operations
can be rewritten via products and Hopf algebras which have been used for
building up renormalised models. These models provide a suitable topology for
solving singular SPDEs. This new construction sheds a new light on these
products and open interesting perspectives for the study of singular SPDEs in
connection with B-series.
