I encountered similar situations.

1. P2P itself is not illegal. German law considers that sharing content protected by copyright is illegal. You can share non-protected content, like let's say an .iso image of a public Linux distribution. Simply using P2P does not violate anything.

2. If they can prove that you did download copyright protected files, then yes, fines are possible, but not that easy. German courts have stated that the owner of the internet access is in theory responsible for any wrong-doings happening on that network and that it is their duty to secure them.

3. An IP address does not represent a person. Legally, an accusation based on IP-only does not stand. That IP can be hijacked by malware or another person can be behind the terminal using it when the offense is done.

4. The notice you got can be considered blackmail. I put it under blackmail because the letter is sent by law firms (that hire specialized third-party services that are scanning P2P nodes and clients, recording IP adresses that are currently downloading illegally in Germany, after which they are authorized by law to ask your internet provider to disclose any information linked to that IP adress), which in turn are hired by companies owning the copyrighted items. So it's a 3rd party involved. Basically, the letter is a warning to let you know that this 3rd party entity knows what you did and if you do not want to go to court you should pay a fine.

5. Given (4), such a case would rarely reach a court because of (3) and other aspects.

Conclusion: Ignoring it would be the recommended choice is this situation. You'll probably never hear from them again, unless you repeat the offense, in which case they will dig more into the matter and they could gather more evidence that (3), which will make the basics for a possible legal case.

I encountered similar situations.

1. P2P itself is not illegal. German law considers that sharing content protected by copyright is illegal. You can share non-protected content, like let's say an .iso image of a public Linux distribution. Simply using P2P does not violate anything.

2. If they can prove that you did download copyright protected files, then yes, fines are possible, but not that easy. German courts have stated that the owner of the internet access is in theory responsible for any wrong-doings happening on that network and that it is their duty to secure them.

3. An IP address does not represent a person. Legally, an accusation based on IP-only does not stand. That IP can be hijacked by malware or another person can be behind the terminal using it when the offense is done.

4. The notice you got can be considered blackmail. I put it under blackmail because the letter is sent by law firms (that hire specialized third-party services that are scanning P2P nodes and clients, recording IP adresses that are currently downloading illegally in Germany, after which they are authorized by law to ask your internet provider to disclose any information linked to that IP adress), which in turn are hired by companies owning the copyrighted items. So it's a 3rd party involved. Basically, the letter is a warning to let you know that this 3rd party entity knows what you did and if you do not want to go to court you should pay a fine.

5. Given (4), such a case would rarely reach a court because of (3) and other aspects.

Conclusion: Ignoring it would be the recommended choice is this situation. You'll probably never hear from them again, unless you repeat the offense, in which case they will dig more into the matter and they could gather more evidence than (3), which will make the basics for a possible legal case. If you also received a document named "Unterlassungserklärung" you should not sign it as doing that would be an admission of guilt, which would give them a lot more legal ground to pursue things further.