  The study of the topology of real algebraic varieties dates back to the work
of Harnack, Klein and Hilbert in the 19th century; in particular, the isotopy
type classification of real algebraic curves in real toric surfaces is a
classical subject that has undergone considerable evolution. On the other hand,
not much is known for more general ambient surfaces. We take a step forward in
the study of topological types classification of real algebraic curves on
non-toric surfaces focusing on real del Pezzo surfaces of degree $1$ and $2$
with multi-components real part. We use degeneration methods and real
enumerative geometry in combination with variations of classical methods to
give obstructions to topological types and to give constructions of real
algebraic curves with prescribed topology.
