Hello,
I am new in electronics and i just want to understand the output different between analog multivabrator (circuit with 2 transistors a couple of resistences) and the 555 timer multivabrator.
I know that the 555 timer provide a square output wave, but can't also the multivabrator circuit provide a square output wave??? And if so, why is that the multivabrator crcuit is sometimes used to trigger the 555 timer???

 

555's and it's dual counterpart, the 556, are very popular and versatile. A 555 has 23 transistors a couple diodes and 16 resistors all in one package.

The 555 can be used for a lot of things besides just a square wave output. Do a search for "NE555 Datasheet" and have a look.

It can be set up for monostable (one-shot) or astable modes (oscillator). Sure, you could trigger a monostable 555 with an external circuit. Or you could use a 556 timer, one side in monostable, the other side astable, and have the one side trigger the other - or myriad other combinations.

A 555 will be inherently more stable over temperature and more reliable than discrete components, not to mention the cost and space savings. You can run them at speeds exceeding 500 kHz, or at small fractions of Hz.

Various datasheets will have a variety of sample applications shown.

Get a couple of these handy circuits and experiment with them

If you want an easy-to-read guide on these, I suggest picking up this book:
"Timer, Op Amp & Optoelectronic Circuits & Projects" by Forrest M. Mims III
It used to be available via Radio Shack in the Engineer's MiniNotebook series as catalog number 62-5032, but it seems they've discontinued Forrest's great books to make room for cell phones
It has 26 pages of example project circuits using just the 555/556 timers and a few additional components.
You can still find it online.

 

The two transistor circuit can indeed produce a square wave. One simply need select component values to over-drive the transistors.

Using one multivibrator to drive another is a technique for producing controlled pulse width. The first mv is running as an astable and the second as a monostable. Varying the second mv is one way to accomplish pulse-width modulation.