Hybridization: the process of combining two complementary single-stranded DNA or RNA molecules and allowing them to form a single double-stranded molecule through base pairing
Introgression: the transfer of genetic information from one species to another as a result of hybridization between them and repeated backcrossing. 
Hybridization introgression occurs when two species hybridize and and one of the species transfers its genetic information to another. This has implications for invasive species management. For example, if an introduced species is alike enough to hybridize with a native species that has a small population, there is a possibility that introgressive hybridization will occur. This can cause the native species to pass its genetic information to the non-native species and in dramatic cases can cause extinction.
The common way to detect if introgression occurs between two species is by looking at the phylogenetic trees of specific genes. If the trees are in conflict then introregression is occurring. This is not always accurate because phylogenetic trees may vary for other reasons. A more accurate way to tell if introgression is occurring is to look at sequence data for multiple individuals per species. If the sequence data becomes more similar over time than it can be said that introgressive hybridization is present in the system. 
Baack, E. J., & Rieseberg, L. H. (2007). A genomic view of introgression and hybrid speciation. Current Opinion in Genetics & Development, 17(6), 513–518. doi:10.1016/j.gde.2007.09.001
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