Comparison Query operators

Name	Description
$gt	Matches values that are greater than the value specified in the query.
$lt	Matches values that are less than the value specified in the query.
$gte	Matches values that are greater than or equal to the value specified in the query.
$lte	Matches values that are less than or equal to the value specified in the query.
$ne	Matches all values that are not equal to the value specified in the query.
$in	Matches any of the values that exist in an array specified in the query.
$nin	Matches values that do not exist in an array specified to the query.

Logical Query operators

Name	Description
$and	Joins query clauses with a logical AND returns all documents that match the conditions of both clauses.
$not	Inverts the effect of a query expression and returns documents that do not match the query expression.
$or	Joins query clauses with a logical OR returns all documents that match the conditions of either clause.
$nor	Joins query clauses with a logical NOR returns all documents that fail to match both clauses.

Element Query operators

Name	Description
$exists	Matches documents that have the specified field.
$type	Selects documents if a field is of the specified type.

Evaluation Query operators

Name	Description
$mod	Performs a modulo operation on the value of a field and selects documents with a specified result.
$regex	Selects documents where values match a specified regular expression.
$where	Matches documents that satisfy a JavaScript expression.

Query operator Array

Name	Description
$all	Matches arrays that contain all elements specified in the query.
$elemMatch	Selects documents if element in the array field matches all the specified $elemMatch conditions.
$size	Selects documents if the array field is a specified size.

Projection operator

Name	Description
$	Projects the first element in an array that matches the query condition.
$elemMatch(projection)	Projects the first element in an array that matches the specified $elemMatch condition.
$slice	Limits the number of elements projected from an array. Supports skip and limit slices.

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Source: http://www.w3resource.com/mongodb/mongodb-query-and-projection-operators.php