Jet-cooled diatomic AlMn has been spectroscopically investigated and is shown to possess a (IIi)-I-5 ground state deriving from the Al (3s(2)3p(1),P-2(0))+Mn (3d(5)4s(2), S-6) separated atom limit. This implies that the aluminum atom favors a 3p pi approach to the manganese atom, a result that is in agreement with previous studies on the related AlCa and AlZn molecules. The ground state bond length has been measured as 2.6384-+0.0010 Angstrom, a value which includes corrections due to spin-uncoupling effects in the X (IIi)-I-5 state. It is suggested that the (IIi)-I-5 state emerges as the ground state due to a particularly favorable configuration interaction with a low-lying (IIi)-I-5 state that derives from the interaction of Al (3s(2)3p(1),P-2(0))+Mn [3d(6)(D-5)4s(1),D-6]. Combination of the atoms in this exited state leads to a strong sigma(2) covalent bond via a 3p sigma(Al)-4s sigma(Mn) interaction, which causes this excited electronic state to drop in energy so that it is expected to lie within a few thousand cm(-1) of the ground electronic state. Following a discussion of the spectroscopic results on AlMn, an overall summary of the spectroscopic results on the 3d series of transition metal aluminides is presented, along with predictions of the ground electronic states of the as yet unobserved AlSc, AlTi, and AlFe molecules.