As far as marriage is a concern, Allah says in Qur'an in Surah Nisa Chapter 4 Verse No 20-25 that those marriages which are prohibited like you cannot marry your mother, your daughter, the sister of your father, sister of your mother and the list is given of your close mahram but marrying the first cousin is permitted.

Today science tells us that directly if you marry the blood brother and sisters, there are high chances of abnormalities there can be genetic problems so directly brother and sister marry, father and daughter, mother and son if they marry or direct paternal uncle ,etc there are high percentage chances of abnormalities so Islam prohibited this .but as far as the first cousin is concerned Islam permits it.

Today science tells us that even in first cousin chances is there but it's negligible
.Genetic problem can even come if two people boy and girl even they are unknown, even if they are not relatives yet there can be genetic problem in them , that doesn't mean genetic problem only comes in relatives, Yes chances are very high if they are direct blood brothers and sisters, mother and father, direct uncle but the first cousins the chances are little bit more as compare to unknown but the difference is exorbitant even, therefore according to hadith in which Prophet said that don't marry continuously generation after generation amongst your first cousin, so generations after generation keep on marring than there is a problem otherwise even medical science says generally its no problem but generation after generation if you keep on doing this, the first cousin marrying with the first cousin and again with the first cousin than a chance rises a bit otherwise normally there is no problem at all.