Change the structure of the home

I need to show at the main page the last 3 articles wrote in each category, for example it should be something like this:
———-
CATEGORY 1
>> Article 2 of category 1 (x comments)
>> Article 1 of category 1 (x comments)

CATEGORY 2
>> Article 3 of category 2 (x comments)
>> Article 2 of category 2 (x comments)
>> Article 1 of category 2 (x comments)

CATEGORY 3
>> Article 3 of category 3 (x comments)
>> Article 2 of category 3 (x comments)
>> Article 1 of category 3 (x comments)
———
How can I do it?
Thanks in advanced!