  We highlight a general theory to engineer arbitrary Hermitian tight-binding
lattice models in electrical LC circuits, where the lattice sites are replaced
by the electrical nodes, connected to its neighbors and to the ground by
capacitors and inductors. In particular, by supplementing each node with $n$
subnodes, where the phases of the current and voltage are the $n$ distinct
roots of \emph{unity}, one can in principle realize arbitrary hopping amplitude
between the sites or nodes via the \emph{shift capacitor coupling} between
them. This general principle is then implemented to construct a plethora of
topological models in electrical circuits, \emph{topolectric circuits}, where
the robust zero-energy topological boundary modes manifest through a large
boundary impedance, when the circuit is tuned to the resonance frequency. The
simplicity of our circuit constructions is based on the fact that the existence
of the boundary modes relies only on the Clifford algebra of the corresponding
Hermitian matrices entering the Hamiltonian and not on their particular
representation. This in turn enables us to implement a wide class of
topological models through rather simple topolectric circuits with nodes
consisting of only two subnodes. We anchor these outcomes from the numerical
computation of the on-resonance impedance in circuit realizations of
first-order ($m=1$), such as Chern and quantum spin Hall insulators, and
second- ($m=2$) and third- ($m=3$) order topological insulators in different
dimensions, featuring sharp localization on boundaries of codimensionality
$d_c=m$. Finally, we subscribe to the \emph{stacked topolectric circuit}
construction to engineer three-dimensional Weyl, nodal-loop, quadrupolar Dirac
and Weyl semimetals, respectively displaying surface and hinge localized
impedance.
