I understand Rosh Hodesh Adar but not the last abreviation. What does it mean? I need to know the meaning of each letter of this abreviation.
The year is a gematria:
ת = 400 ש = 300 ע = 70 ה = 5
which adds to 775.
The 'ה prefix presumably is indicating the thousands although this is usually omitted when quoting a year. However 4775 would of course also be תשעה
There are no letters that correspond to numbers above 400 so we actually combine two and add them together.
I have seen some actually assign final-letters to these values so
ך=500 ם=600 ן=700 ף=800 ץ=900
This isn't universally accepted, for example, when you calculate the gematria value of a word, you normally count final letters as the same score to their regular version, e.g. a final "mem" would score 40 like a regular "mem".
Gematria is directly referred to in Talmud so is certainly not new. There are hints of it in chumash too e.g. "im laval garti" where "garti" has a gematria of 613, the number of Mitzvot (thus Yaakov is hinting he kept the commandments) however these are just hints and there is no direct reference to Gematria being used.
תשע"ה is not an abbreviation, rather it is a number. Each Hebrew letter corresponds to a number, this is known as Hebrew Numerals see: http://en.wikipedia.org/wiki/Hebrew_numerals
In this instance the numbers refer to the year in the Hebrew calendar 5775 Thus, it says the first of Adar of the year 5775 (ie. 5775 years since creation)