Let's Encrypt
Let's Encrypt is a certificate authority operated by the Internet Security Research Group. It freely issues certificates (rate limits apply) and publicly advocates for encryption of all web traffic.
For details on certbot(1), their interface for certificate generation, see here.
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Certificates
To see a historical log of certificates issued, search https://crt.sh. Domains can be queried as https://crt.sh/?q=example.com.