**PostgreSQL - All Index Types:**

```sql

-- 1. B-tree (default)

CREATE INDEX idx_btree ON orders(order_date);

-- Same as:

CREATE INDEX idx_btree ON orders USING btree(order_date);

-- Multi-column B-tree

CREATE INDEX idx_customer_date ON orders(customer_id, order_date);

-- Use for: WHERE customer_id = ? AND order_date > ?

-- 2. Hash index

CREATE INDEX idx_hash ON users USING hash(email);

-- Only for: WHERE email = 'exact@match.com'

-- NOT for: WHERE email LIKE '%match%'

-- 3. GIN index for full-text

CREATE INDEX idx_gin_fts ON articles

USING gin(to_tsvector('english', content));

-- Query with:

SELECT * FROM articles

WHERE to_tsvector('english', content) @@ to_tsquery('postgresql & performance');

-- GIN for JSONB

CREATE INDEX idx_gin_json ON products USING gin(metadata);

-- Query with:

SELECT * FROM products WHERE metadata @> '{"brand": "Apple"}';

SELECT * FROM products WHERE metadata ? 'warranty';

SELECT * FROM products WHERE metadata ?& ARRAY['color', 'size'];

-- GIN for arrays

CREATE INDEX idx_gin_array ON posts USING gin(tags);

-- Query with:

SELECT * FROM posts WHERE tags @> ARRAY['postgresql'];

SELECT * FROM posts WHERE tags && ARRAY['sql', 'database'];

-- 4. GiST index for geometry

CREATE INDEX idx_gist_geo ON locations USING gist(coordinates);

-- Query with:

SELECT * FROM locations

WHERE ST_DWithin(coordinates, ST_MakePoint(-122.4, 37.8), 5000);

-- GiST for range types

CREATE INDEX idx_gist_range ON bookings USING gist(booking_period);

-- Query with:

SELECT * FROM bookings

WHERE booking_period && '[2024-01-01, 2024-01-31)'::daterange;