  Weyl points in three spatial dimensions are characterized by a
$\mathbb{Z}$-valued charge -- the Chern number -- which makes them stable
against a wide range of perturbations. A set of Weyl points can mutually
annihilate only if their net charge vanishes, a property we refer to as
robustness. While nodal loops are usually not robust in this sense, it has
recently been shown using homotopy arguments that in the centrosymmetric
extension of the $\textrm{AI}$ symmetry class they nevertheless develop a
$\mathbb{Z}_2$ charge analogous to the Chern number. Nodal loops carrying a
non-trivial value of this $\mathbb{Z}_2$ charge are robust, i.e. they can be
gapped out only by a pairwise annihilation and not on their own. As this is an
additional charge independent of the Berry $\pi$-phase flowing along the band
degeneracy, such nodal loops are, in fact, doubly charged. In this manuscript,
we generalize the homotopy discussion to the centrosymmetric extensions of all
Atland-Zirnbauer classes. We develop a taylored mathematical framework dubbed
the AZ+$\mathcal{I}$ classification and show that in three spatial dimensions
such robust and multiply charged nodes appear in four of such centrosymmetric
extensions, namely AZ+$\mathcal{I}$ classes $\textrm{CI}$ and $\textrm{AI}$
lead to doubly charged nodal lines, while $\textrm{D}$ and $\textrm{BDI}$
support doubly charged nodal surfaces. We remark that no further crystalline
symmetries apart from the spatial inversion are necessary for their stability.
We provide a description of the corresponding topological charges, and develop
simple tight-binding models of various semimetallic and superconducting phases
that exhibit these nodes. We also indicate how the concept of robust and
multiply charged nodes generalizes to other spatial dimensions.
