Hochschild homology and cohomology for involutive $A_{\mathrm{\infty }}$-algebras

We present a study of the homological algebra of bimodules over $A_{\mathrm{\infty }}$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_{\mathrm{\infty }}$-algebras.