I hope that you find this both interesting and informative :
https://www.rfglobalnet.com/doc/understanding-antenna-gain-beamwidth-and-directivity-0001
However, one small item that confuses many people is that there is lack of clarity when discussing dB values and i want to point out that antenna gain is this article specifically is calling out gain in dB as POWER and not voltage.
The log function of power is P = 10 log x and thus for every -3dB demarcation, there is a reduction in power by 1/2.
If it is +3dB gain, then the power is 2 times, relative to an isotropic (spherical) point antenna (both imaginary and ideal).
Also what is cool about this article is that it showcases some of the types of antennas and a perspective on what each has in gain relative to an isotropic antenna in dBi.