Corrections in red.  Stylistics in blue.

This's [1] my first notebook entry

I'm Roman. I'm from Russia. I'm 25, and tomorrow will be 26 years old.  [2]

I'm in my last year at the Mining University of Saint-Petersburg.

And I work in the Scientific-Research-Institute.

I love sports, good books, hip-hop, and electronic genres of music.

To be continued...

[1] "This's" is not "wrong," but it is nonstandard and informal.  

[2]  Variant:  ... and tomorrow I'll turn 26.