Q:

Should I quit during probation immediately or first discuss problems with my manager? 

I started a new software developer job two months ago with a probation period of six months. 
Unfortunately I am quite dissatisfied with the company and management.  I'm a young and very passionate developer and feel like I cannot make use of my full potential.  There is also no one more skilled than me to teach me new things.  Therefore I am thinking of leaving the company as soon as I found a new position.  What I am thinking about, however, is if I should first discuss my problems with my manager.  He told me to do so if I face any problems. 
Should I talk to my manager first or start looking for a new job immediately and then just quit? 
EDIT
I received a lot of critic in comments and answers concerning several things. 

being overconfident
being high-maintenance
having low communication skills
doing a poor job during the initial interview

I could try to defend myself and explain in a lengthy edit to my question why some of these accusations are definitely false.  This, however, would not help to improve the question nor the answers and would be off topic.  Your thoughts made me think about my situation nevertheless and some of them might be true. 
Unfortunately most of the answers - while mentioning good points - did not really answer my original question.  It looks like there was a misunderstanding.  I did not intend to ask if I should quit my job before having found a new one.  I also did not intend to ask if I should my quit my job at all.  I intended to ask whether one should start looking for a new job when unsatisfied during probation or if one should first talk to the manager.  Everything else was an attempt to explain that I see only a low chance that talking to my manager would change the situation significantly. 

A:

If I talk to him I guess he would listen carefully but not understand
  much of it (that is exactly one of my concerns).  Other team members
  would not care much about my suggestions (Code reviews, CI server,
  static code analysis, consistent style guidelines) so I doubt that any
  of them would get heard.  If I then quit this would create quite some
  tension. " You don't do what I demand, so I quit". 

If you are already convinced that your manager won't understand what you are saying, that's a big problem.  You seem to have already "flipped the bozo bit" as some like to say. 
Either your communication skills are poor, or you are saying that your manager isn't smart enough.  Without having discussed these sorts of issues yet, you may have come to an unsupported conclusion - but there's only one way to know for sure. 

However, if I talk to him even if he would totally agree with me and
  promise to fix all of my concerns it would take several months until
  the transition would be completed if not even more than a year.  I am
  not sure if I am willing to wait that long.  But if I quit during this
  transition I could be considered impatient or spoilt. 

You've only been there 2 months so far.  And you aren't willing to wait "several months" to see your concerns "fixed". 
Again, it sounds like your mind is already made up. 

If I just quit immediately I think this would come out of nowhere for
  my manager and therefore leave a bad impression of me with him.  As my
  feeling is that he does not put much past me my fear is that he would
  think I quit because the job was to hard for me (quite the opposite is
  the case). 

The only way your quitting would come out of nowhere is if you don't discuss your concerns with your manager.  
If you really don't want to leave a bad impression, you know what you should do. 

Should I talk to my manager first or quit immediately? 

Find a new job first. 
During your interviews, make sure to ask enough questions so that you'll know it has everything you want (code reviews, CI server, static code analysis, consistent style guidelines, whatever).  Apparently you did a poor job at digging in this time - you don't want to repeat that mistake. 
Then, once you get a new job offer and acceptance, give an appropriate notice and leave on a good note.  Probation periods are for both sides to see if there is a good fit or not.  You've already decided the "not" part. 
Since you haven't felt it necessary to discuss the issues you are seeing with your current manager, and since you appear to already have mentally checked-out of this job, it's probably not worth talking to your manager. 

A:

There is also no one more skilled than me to teach me new things. 

You should stay until you get a better offer. 
If you feel this company isn't a good fit for you, it might be wise to start looking for a new job.  Based on the quote above, it seems like this would be wise.  Finding a company with people working at your approximate skill level is key to happiness in the workplace.  However, the first 2 months of a job rarely give good insight to how you will feel after 6 months.  
You should talk to your manager. 
Your concerns could be very helpful to them, and they might implement them, but only if you bring them up.  However, I will caution that often young developers push topics like style/convention, but this is generally not in the interest of the company and so is typically not implemented.  Code convention is for future development, not past.  You can find many questions on here about this topic.  I will say that you ought to try listening to your manager/team's concerns.  They may be more competent than your first impressions have led you to believe. 

I could be considered impatient or spoilt. 

This is none of your concern if you quit, and it is likely untrue.  Employers understand that not everyone they hire will be a perfect fit.  Unless you think they are likely to and capable of sabotaging your future career, their opinion of you after you quit is moot. 

A:

I know how you feel because I was in a very similar situation when I graduated (and it wasn't that long ago).  As a young and inexperienced dev I didn't really know what to look for in an employer.  In fact, I felt that interviews were essentially one sided examinations, and that I should count myself lucky that any employer would hire me (especially for a decent salary). 
This mentality of being grateful to simply have a decent paying job, as well as the mentality to just try my best even if things are going less than "great", lead me to stick around with that first company for a lot longer than I should have.  And it cost me. 
That workplace taught me a lot, but I still ended up falling behind on key skills and technologies, because I received absolutely ZERO mentorship, and the technology stack and development process there both left a lot to be desired.  Looking back, I regret sticking around as long as a I did. 
Since then, I've learned to trust my instinct and move on from a job when I feel that the experience I'm gaining is stale, or otherwise not enriching my resume, or improving my future employability. 
Some things which I would recommend:
1.  Read up on interview tactics and negotiations. 
Understand that interviews are an opportunity for you to assess your potential employer, as much as it is an opportunity for them to test your own knowledge and skills.  Don't be afraid to ask pointed questions regarding their development process, or even asking to sit down with one of their tech guys and quizzing him for a few minutes. 
2.  Pick your goals and targets
Check out what the latest technologies are.  Which are you interested in?  Which are gaining popularity, and generating well paid jobs?  Once you've decided what you want to work with don't be afraid to start learning those technologies on your own, and going out and finding companies which use them. 
Don't just take any job if you can possibly afford to keep looking for one which will allow you to work with the technology stack you're interested in! 
3.  Listen to your instincts
I'm not advising you to jump from job to job willy nilly.  However, if you feel that a workplace has nothing left to offer you, don't be afraid to get out. 
My rule of thumb is that if a year passes without my work offering me any opportunities to learn something new,or otherwise enrich my resume, I start looking for something new.  Of course that "something new" should also be relevant to the career path which you envision for yourself. 
4.  Conclusion
If this company's development process and technology stack is lacking, you should start looking for something new.  As a junior developer it would be invaluable for you to find a job where mentorship and code reviews are actually a part of their culture. 
Don't fall into the trap of thinking that you might magically change this place for the better.  Simply start looking for a job which will allow you to grow.