What are advantages and disadvantages of using a Barlow lens?

Some major advantages:

Achieve higher magnifications.

Provide flexibility of magnification levels with your existing eyepieces. For example, if you have 2 Plössl eyepieces with 16mm and 26mm focal length and use them on a telescope with 800mm focal length, you have a 800/16=50x and 800/26=31x magnification levels respectively. With a 2x Barlow lens, you will get 100x and 62x magnifications as well.

Increase eye relief (distance of exit pupil from eye lens). Many eyepieces have an eye relief which is directly related to its focal length. For example, the eye relief of a Plössl is 0.73 x its focal length. Therefore, for these eyepieces, there will be a greater eye relief with a Barlow than without one.

Disadvantage: a major disadvantage of adding a Barlow is a slightly decreased brightness in the produced image.