The most important aim of a Muslim is to win the Pleasure and Good-Will of Almighty Allah by sincerely following the commands of Almighty Allah and obeying the teachings of the last prophet Hazrat Muhammad SAW).
In Islamic countries.
The question as written makes no sense. If you mean "What was the most important Muslim scientific achievement?", see the Related Question below.
Prophet Muhammad (PBUH)
haaj
My most important aim and task is providing for my family and living a good life before God.
universities
universities
I don't know about most important but Hinduism is the third most popular religion in the world
The most important day is the 9th day or the Day of Arafaat. Every Muslim must fast it.
Algebra
Muhammad is not Hindu, he is Muslim. His most important teaching (for Islam) is usually believed to be the Unity of God or Tawhid.
The most important example on Muslim mathematics is Al-Khawarezmi who had so many great achievements in mathematics like for instance inventing algebra.