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.