Courts: Criminal Proceedings

Recently, I saw a court show on TV about a penal case. Did I correctly see, that there was no jury?

Yes, you correctly saw no jury and you will never see one in a German court. The German legal system did not apply the concept of installing juries. The judge is the person to be convinced.  
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I heard that there was supposed to a criminal investigation running against me. What can / am I to do about it?

What should you do about it? In Germany, as well as in other democratic countries there is the principle of innocence. Until a criminal court sentences you, you are innocent. If the police finds a “starting suspicion” they will investigate. If not, then not. If they do find grounds that they think is worth following, they will report to the district attorney and he will decide if this suspicion is worth a criminal case or not. 
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So what happens if the state attorney opens a criminal case?

He will investigate if the presented facts create grounds for a penal complaint in court. If he is convinced that you have committed a crime, he will file a complaint in court. When in penal court, the judge will decide if he follows the district attorney or not. If not, then the case will be closed. If the complaint convinces him, he will open a proceedings in court and summon you to trial.
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What is the procedure of a penal case trial?

The judge opens the trial by calling everyone to order and officially acknowledges the presence of the defendant, his attorney, district attorney, and any witnesses. The judge will interview you on your personal details. Then the state attorney stands up and reads aloud the complaint. You will now be asked what your arguments are in this dispute. In the mean time, all witness will have been dismissed to wait outside. After the defendant and state attorney have argued and listened to witnesses, the judge will announce a sentence – with or without a recess. In Germany, there is no cross examination and no jury to be convinced.
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Additional information