Transmittance
This parameter controls the color of the light when it passes through a transparent material. Choose a Transmittance color by clicking on the color picker, or specify a texture by clicking on the texture button. The Transmittance color represents the color of the light when it has reached the Attenuation distance (see below).
Note: Transmittance must be a color other than black for transparency to appear. Setting a brighter transmittance color results in clearer transparency, but you should remember that this parameter is also tied to the Attenuation Distance.
Attenuation
Glass, water, or even air are transparent when thin, but become opaque when a specific thickness is reached (different for each material). As light travels through a material, it loses energy. The Attenuation distance parameter allows you to specify how far light can move through an object before losing half its energy. For example, if you have a 2cm thick glass window and you set the attenuation distance to 2cm, the light shining through the glass on the other side will be half as bright.
Attenuation distance and Transmittance work together. You must set the Transmittance color higher than RGB 0 for the Attenuation distance to become active. If your Attenuation distance is very small (for example 1nm) the object will remain opaque because the light can only travel a very small distance into the object, and will not come out on the other side. On the other hand, if you have a 1cm thick glass window and you set the attenuation distance very high (for example 900 meters), and you set the Transmittance color to blue, the glass will not be colored blue at all. It will be completely transparent because there was not enough distance in the 1cm thick glass to cause any attenuation and reveal the Transmittance color.
Attenuation is ruled by an exponential curve, therefore: the thicker the object, the more attenuated the light will be.
To better understand the concept of Attenuation, consider sea water. When the water layer is very thin (like water in the palm of your hand) you do not see attenuation: the water looks transparent. When you have more water thickness, you see a typical sea color (grey, dark-blue or light blue-green, depending on deep or shallow waters). The Transmittance color represents the color that you want to get approximately at the Attenuation distance. Beyond this distance, the light is more and more attenuated, it loses more and more energy, and the view eventually turns opaque if the volume is thick enough.
Abbe
Different wavelengths of light can be refracted at slightly different angles as they pass through a material, and this is what causes dispersion, the effect seen when a beam of light passes through a prism and is split up into the different wavelengths of light.
The name Abbe comes from the German physicist Ernst Abbe, who defined the Abbe number.
Abbe value controls the amount of dispersion. The higher the Abbe number, the less dispersion will be visible in the render. An Abbe number higher than 60-70 will render as if dispersion was not activated.
Note: Dispersion must be enabled in the Material Properties panel; otherwise the Abbe parameter in the BSDF will be grayed-out. Because dispersion generally takes longer to render, it is disabled by default.