1. Temperature: This is the most fundamental property. A star's temperature determines its color, with hotter stars appearing blue-white, while cooler stars appear red. Temperature is also linked to a star's luminosity and spectral class.

2. Luminosity: This refers to the total amount of energy a star emits per second. Luminosity is closely related to a star's size and temperature.

3. Spectral Class: This categorizes stars based on their surface temperature and the elements present in their atmospheres. The most common classification system is the OBAFGKM system, with O being the hottest and M being the coolest.

4. Mass: A star's mass is a crucial factor determining its lifespan, luminosity, and evolution. More massive stars have shorter lifespans and are significantly brighter than less massive stars.

While these are the most fundamental properties, other factors can be used for classification, such as:

* Size (radius): Stars come in a wide range of sizes, from small red dwarfs to giant supergiants.

* Composition: The elements present in a star's atmosphere can also be used for classification.

* Age: Stars evolve over time, changing their temperature, size, and luminosity.

* Distance: While not a property of the star itself, distance is important for understanding its apparent brightness and true luminosity.