ISIC – International Student Identity Card. This is the ONLY legitimate international document proving student status. The ISIC entitles you to all discounts and conveniences available for students all over the world.

Eligibility Terms
The ISIC is issued to full-time students (including students at foreign universities), doctoral students, interns, post-graduate students, high-school students who have completed the 7th grade, and participants in educational courses (mostly language ones) organized by an accredited educational institution in the country or abroad, lasting at least 12 weeks, at an intensity of no less than 15 classes weekly.

Validity Term
September 1st to December 31st the following year, (i.e., from September 1st, 2002 to December 31st, 2003).

Advantages
Holders of an ISIC are entitled to travel at special student flight fares (SATA) as well as receive all other discounts (about 200 000), sanctioned by the international authorities (including in Bulgaria), in the following categories: travel (including 50% off when traveling with the Bulgarian State Railways - БДЖ), hotels and hostels, museums and places of interest, restaurants and pubs, shopping, sports and beauty centers, services, computers and telecommunications, education.
Information on discounts around the world: http://www.isic.org/sisp/index.htm?fx=isic.discounts
24-Hour ISIC Emergency Help Line: http://www.isic.org/sisp/index.htm?fx=s ... pline.html

Documents Required for Obtaining an ISIC card
For students in Bulgaria: a certificate issued by the respective educational institution (уверение), OR a genuine student markbook (студентска книжка) along with copies of its first page and the page showing the last completed semester.
For students studying abroad: respective documents from university.
For high-school students: high-school identity card or certificate, a markbook.
For post-graduate and doctoral students: respective certificates of full-time education.
For language course participants: a document showing the course’s duration and intensity.
Please make sure to bring a recent photo, your passport, or an identity card.

Price: 10 BGN

You can have ISIC cards issued in any USIT COLOURS office. Click here for a full list of USIT COLOURS offices throughout Bulgaria - http://www.usitcolours.bg/contacts.php?ch=2

Sources:
http://www.isic.bg/
http://www.isic.org/sisp/index.htm
http://www.usitcolours.bg/

Sofia University doesn't seem to be in their list. http://www.isic.bg

It's not, but that doesn't mean Sofia University students can't get ISIC cards.

Of course, they can steal ISIC cards.

за колко време ги вадят и къде се получават

They're being issued on the spot. You can have ISIC cards issued in any USIT COLOURS office. Click here for a full list of USIT COLOURS offices throughout Bulgaria - http://www.usitcolours.bg/contacts.php?ch=2