The present invention relates to an electrical machine (1) having a housing (2), wherein the housing (2) has a hollow-cylindrical cooling jacket (2a) for accommodating a stator (3) and, attached to the end sides of the cooling jacket (2a), housing closures (2b), in particular mounting plates, and wherein the cooling jacket (2a) has cooling ducts (4a) running between its end sides (17) and the housing closures (2b) have redirection grooves (4b) so that two adjacent cooling ducts (4a) are fluidically connected by a redirecting groove (4b), whereby the cooling ducts (4a) and the redirecting grooves (4b) form a meandering cooling path (10) which extends through the housing (2) between an inlet (5) and an outlet (6) and through which a coolant can flow, wherein the housing (2) has a bypass duct (7) which fluidically connects the inlet (5) and the outlet (6) while bypassing the meandering cooling path (10), or which fluidically connects two part regions of the meandering cooling path (10) while bypassing one part of the meandering cooling path (10).