From where does the MySQL Query Optimizer read index statistics? I'm trying to determine from where the MySQL optimizer obtains the list of indexes that are available for a table when it estimates the cost of (prepares) a query from.
The direct answer for this would be 

information_schema.statistics

mysql&gt; desc information_schema.statistics;
+---------------+---------------+------+-----+---------+-------+
| Field         | Type          | Null | Key | Default | Extra |
+---------------+---------------+------+-----+---------+-------+
| TABLE_CATALOG | varchar(512)  | NO   |     |         |       |
| TABLE_SCHEMA  | varchar(64)   | NO   |     |         |       |
| TABLE_NAME    | varchar(64)   | NO   |     |         |       |
| NON_UNIQUE    | bigint(1)     | NO   |     | 0       |       |
| INDEX_SCHEMA  | varchar(64)   | NO   |     |         |       |
| INDEX_NAME    | varchar(64)   | NO   |     |         |       |
| SEQ_IN_INDEX  | bigint(2)     | NO   |     | 0       |       |
| COLUMN_NAME   | varchar(64)   | NO   |     |         |       |
| COLLATION     | varchar(1)    | YES  |     | NULL    |       |
| CARDINALITY   | bigint(21)    | YES  |     | NULL    |       |
| SUB_PART      | bigint(3)     | YES  |     | NULL    |       |
| PACKED        | varchar(10)   | YES  |     | NULL    |       |
| NULLABLE      | varchar(3)    | NO   |     |         |       |
| INDEX_TYPE    | varchar(16)   | NO   |     |         |       |
| COMMENT       | varchar(16)   | YES  |     | NULL    |       |
| INDEX_COMMENT | varchar(1024) | NO   |     |         |       |
+---------------+---------------+------+-----+---------+-------+
16 rows in set (0.01 sec)


You could SELECT from that table with

SELECT * FROM information_schema.statistics
WHERE table_schema='mydb' AND table_name='mytable';


or see the statistics by doing

SHOW INDEXES FROM mydb.mytable;

Please keep in mind that this table is not always accurate in a write-heavy environment. Periodically you will have to run ANALYZE TABLE against all MyISAM tables that are updated frequently.  Otherwise, the MySQL Query Optimizer, which relies on information_schema.statistics, can sometimes make bad choices when developing EXPLAIN plans for queries. Index statistics must be as up-to-date as possible.

ANALYZE TABLE has ABSOLUTELY NO EFFECT against InnoDB tables. All index statistics for InnoDB are computed on demand by means of dives into the BTREE pages. Therefore, when you run SHOW INDEXES FROM against an InnoDB table, the cardinalities displayed are always approximations.

UPDATE 2011-06-21 12:17 EDT

For clarification of ANALYZE TABLE, let me rephrase. Running ANALYZE TABLE on InnoDB tables is completely useless. Even if you ran ANALYZE TABLE on an InnoDB table, the InnoDB storage engine performs dives into the index for cardinality approximations over and over again, thus trashing the statistics you just compiled. In fact, Percona performed some tests on ANALYZE TABLE and came to that conclusion as well.