Indeed, today we will get to know the first part of these prepositions. But before you should know that even Germans frequently confuse the Dativ and the Genitiv case. That's why in the common speech you can possibly hear the wrong declination. There is even a book that deals with this problem:
The book's title is actually a reference to a linguistic phenomenon in certain dialects of German in forming noun phrases showing possession. In these dialects, the qualifying noun, which would be in the genitive case in standard German, is replaced by a noun in the dative case and the qualified noun is preceded by a possessive adjective. For example, instead of saying das Buch des Mannes (the man’s book), one says dem Mann(e) sein Buch ([to] the man his book) or das Buch vom Mann(the book of the man). Thus, the book's title, Der Dativ ist dem Genitiv sein Tod (literally 'the dative is [to] the genitive its death') is a dialectal manner of saying Der Dativ ist der Tod des Genitivs (or Der Dativ ist des Genitivs Tod), which can be translated into English as 'the dative is the genitive's death' (or 'the dative is the death of the genitive').
Further I will mention the most frequent mistake one can run across.
Während (during)
Während der Fahrt hat er geschlafen.
Während des Abends habe ich ihn nicht gesehen.
Anlässlich (on the occasion of)
Anlässlich seines Geburtstages hat er uns alle zu sich nach Hause eingeladen.
Abseits (aside)
Das Haus stand etwas abseits der Straße
Außerhalb (outside)
Der Ball befindet sich außerhalb des Spielfeldes
Wegen (because of)
Wegen des schlechten Wetters fährt die U-Bahn unregelmäßig.
In the common speech in this case Germans sometimes use to say "Wegen dem schlechten Wetter...." and that is wrong.
Trotz (despite, in spite of)
Trotz seiner Niederlage hat er gelächelt
To be continued
Er
