accusative

for 

accusative

against

accusative

without

accusative

around

dative

out of/to come from[cities or countries]

dative

besides/except for

dative

with[at the home of]/at[a place of business]/near[in the proximity of]

dative

with/by means of [transportation]

dative

 to [cities or countries w/o an article]/after

dative

since[time]

dative

from/of/by[author]

dative

to [with people and short distance travel]

for [in certain expressions]

2 way

on[vertical sufaces i.e. walls]

at [the side of]

to [up to the edge of i.e an die Ecke]

2 way

on top of [horizontal surfaces]

to [public space]

2way

behind/in back of

2 way

in/inside[of]

into

to

2way

next to/beside

2way

over/above

across[direction] 

ex. Ich gehe über die Straße.

I walk across the street

2way

under

2way

in front of

2way

between