  We present a consolidated manual of Euclidean gravity approaches for finding
the logarithmic corrections to the entropy of the full Kerr-Newman family of
black holes in both extremal and non-extremal limits. Seeley-DeWitt
coefficients for the quadratic fluctuations of a concern gravity theory appear
to be the key ingredients in this manual. Following the manual, we calculate
the first three Seeley-DeWitt coefficients and logarithmic corrections to the
entropy of extremal and non-extremal black holes in a generalized
Einstein-Maxwell theory minimally-coupled to additional massless scalar,
vector, spin-1/2 Dirac and spin-3/2 Rarita-Schwinger fields. We finally employ
the Seeley-DeWitt data to reproduce the logarithmic entropy corrections for
extremal black holes in all $\mathcal{N} \geq 2$ Einstein-Maxwell supergravity
via an alternative local supersymmetrization method.
