What are the types of temperature inversions?

There are four kinds of inversions: surface, valley, subsidence and frontal.

• Surface temperature inversion: It is developed when air is cooled by contact with a colder surface until it becomes cooler than the overlying atmosphere; this occurs most often on clear nights when the ground cools off rapidly by radiation.
• Subsidence inversion: The air at higher altitudes becomes warmer than at lower altitudes, producing a temperature inversion. This type of temperature inversion is called subsidence inversion.
• Valley inversion: Cold air at the hills and mountains, produced during the night, flows under the influence of gravity. Being heavy and dense, the cold air acts almost like water and moves down the slope to pile up deeply in pockets and valley bottoms with warm air above
• Frontal inversion: When the warm and cold fronts meet, then the warm front rises up and being heavier the cold front sinks down. 

Further Reading:

• Factors Controlling Temperature Distribution
• Geography Notes