On (strongly) ($\mathrm{\Theta }$-)discrete homogeneous spaces

We introduce the classes of (strongly) ($\mathrm{\Theta }$-)discrete homogeneous spaces. We discuss the relationships of these classes to other classes of spaces possessing homogeneity-related properties, such as (strongly) ($n$-)homogeneous spaces. Many examples are given distinguishing discrete homogeneity and other types of homogeneity.