A (unofficial and probably wrong) precis of those 13 Principles:

1. Legality - privacy restrictions must be prescribed by law.

2. Legitimate Aim - What you want to break privacy for must be to support laws.

3. Necessity: We cannot (reasonably) achieve the aim without breaching privacy.

4. Adequacy: Listening to your phone calls must reasonably allow us to achieve the aim.

5. Proportionality: Don't listen to everyone when only some will do.

6. Competent Judicial Authority: Any breach of privacy must be authorised by Independant, capable judges.

7. Due process: Who follow a clear process

8. User notification: and tell you you are being watched (unless that might hurt the Aim)

9. Transparency: We get to see the metadata on their phone tapping

10. Public oversight: and a few of us get to see everything not just the metadata

11. Integrity of communications and systems: backdoors are not allowed, if you are bugging us legally, you dont need a back door

12: Safeguards for international cooperation: No playing arbitrage with different jurisdictions

13: Safeguards against illegitimate access: and secure your stuff.

I hope those help