Is cousin marriage allowed in Islam. Please tell me about cousin marriage and what are the effects of cousin marriage in spouse's new generation medically?

One line answer will be it is allowed, but even islam encourages you to marry outside family and tribes.

Scientifically those who marry in their family, have more chances of having disabled kids.

definitely its allowed. But it is discouraged by science.But if both men and women are medically tested and they are not suffering from any disease like Thalassemia minor or major etc. then its ok. This thing should be checked even if you are marrying out of family.

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Shabdon mein kya tareef karoon aap ki MUSSAA
Aap shabdon mein kahan bandh payenge.
Kabhi mere aankhon mein jhaank kar dekho,
Hazaron alfaz khud-b-khud bikhar jayenge.

Hazrat Ali married to Hazrat Fatima (a cousin marrige). So cousin marriage is allowed in Islam.

Cousin marriage upto one or two generation is ok but later on it should be avoided for the sake of healthy/intelligent new generation.

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/// Aur be ghum hain zamanay main muhabat kay siwa ///

Cousin marriages tend to concentrate the gene pool, and that way restrict genetic diversity to manifest in the population. In other words, dominant genes remain dominant while recessive genes remain recessive for generations in such inter-marriage practising families. Concentration of the gene pool like concentration of power is disapproved of. Incest is strongly condemned for the same reason.
Marrying outside one's family is better because it not only dilutes the gene pool but also brings two different families, two different cultures, two different civilisations in contact with each other, encourages social integration, develops confidence and understanding among various communities and social classes which is necessary for the sense of co-existence and tolerance of foreign traits and in a way uproots xenophobic tendencies in the human psyche.
All those things could be right, but the question is: what if someone falls in love with his/her cousin? Go for it without a backward glance because love is blind.

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