Bitcoin Q&A: Important terminology explained

I am confused by terminology in Bitcoin. Please explain the following terms: private / public keys, hash functions, elliptic curve, addresses, and signatures. How can you create an address offline? How does the Bitcoin network “find out“ about the address? These questions are from the third and fourth sessions of MOOC 12, which took place on September 27th and October 4th 2019. If you want early-access to talks and a chance to participate in the monthly live Q&As with Andreas, become a patron: https://www.