Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.

 

As long as you pray alone, you can pray immediately when the adhan starts. It is recommended you repeat the words after adhan, make supplications, pray nafl and then offer the obligatory prayers.

 

If you are praying in congregation, you should wait for the people to start congregation and join them. For offering fajr when it is still dark, this is the accepted view of the majority of Muslim scholars who based their view on the report of `A’ishah who said, “The Messenger of Allah, may Allah bless him and grant him peace, used to pray Morning prayer and the women would leave wrapped in their garments and they could not yet be recognized in the darkness.” (Al-Bukhari and Muslim)

 

Allah Almighty knows best.