Indexes and B-trees: A sorted, tree-shaped shortcut structure that lets the database find rows without scanning the whole table.
Index selectivity: How narrowly a condition filters the table, the reason a low-selectivity index gets ignored in favor of a full scan.
Query processing and optimization: How the database decides which order to run joins and filters in, to answer a query as cheaply as possible.
Transactions and concurrency
Transactions and ACID properties: The four guarantees (atomicity, consistency, isolation, durability) that make a transaction feel like one indivisible unit.
Concurrency anomalies: The specific bad things that can happen when two transactions run at the same time: dirty, non-repeatable, and phantom reads.
Isolation levels: How much of those concurrency anomalies a database is willing to allow, chosen as a tradeoff against speed.
Conflict-serializability: Checking whether an interleaved schedule of transactions could have happened in some one-at-a-time order instead.
Lock-based concurrency control: Transactions acquiring then releasing locks on data, in two strict phases, to enforce serializability in practice.
Deadlock detection and prevention: Two transactions each waiting on a lock the other holds, and how the database detects or prevents that standoff.
Recovery
Write-ahead logging and recovery: Writing what you're about to change to a log before touching the actual page, so a crash can still recover the right state.
ARIES recovery algorithm: The specific three-phase algorithm (analysis, redo, undo) real databases use to recover using the write-ahead log.
Distributed systems
Distributed databases: A database whose data lives across multiple machines instead of one.
CAP theorem: You can't have perfect consistency, availability, and partition tolerance all at once, pick two.
Consistency models: How strictly a distributed database insists every read sees the latest write, versus allowing some staleness.
Replication and sharding: Copying data across machines for redundancy versus splitting it across machines for scale.
NoSQL data models: Alternatives to tables: documents, key-value pairs, wide columns, or graphs, each suited to a different access pattern.
Analytics
Data warehousing and OLAP: A separate database optimized for big analytical queries over historical data, not fast day-to-day transactions.
Administration
Database security and access control: Who's allowed to see or change what, enforced through roles, privileges, and protection against attacks like SQL injection.