1. Spectral Classification: This method categorizes stars based on their surface temperature and composition. It uses the spectral lines seen in their light, which are unique to specific elements and their ionization states. The spectral classes are:

* O: Hottest, blue, and massive stars with strong lines of ionized helium and oxygen.

* B: Hot, blue-white stars with lines of neutral helium and hydrogen.

* A: Hot, white stars with strong hydrogen lines and weaker helium lines.

* F: Yellow-white stars with prominent lines of ionized metals like calcium.

* G: Yellow stars like our Sun, with strong lines of neutral metals.

* K: Orange stars with strong lines of neutral metals and molecular bands.

* M: Coolest, red stars with strong lines of metal oxides.

Each spectral class is further subdivided into ten luminosity classes, ranging from Ia (supergiants) to VII (white dwarfs), indicating a star's luminosity or intrinsic brightness.

2. Hertzsprung-Russell (H-R) Diagram: This is a graphical representation of luminosity against surface temperature for a large number of stars. It shows how stars of different spectral classes and luminosities are related. The H-R diagram reveals:

* Main sequence: A diagonal band where most stars spend most of their lives, fusing hydrogen into helium in their cores.

* Giant and supergiant stars: Larger, cooler, and more luminous stars located above the main sequence.

* White dwarf stars: Small, hot, and dense stars located below the main sequence.

By combining these two classifications, astronomers can get a comprehensive understanding of a star's physical properties, including its temperature, size, mass, and age.