In thermodynamics, gas laws are a set of equations that describe the behavior of bodies of gas under what are known as ideal, perfect, standard, or non-extreme conditions. The various laws, as listed below, came into existence following the invention of German engineer Otto Guericke’s vacuum pump in 1645, beginning with the experimentations of Irish chemist Robert Boyle. The central law for most gases is the ideal gas law.

Boyle’s law
In 1658, Irish chemist Robert Boyle and his assistant Robert Hooke built a combination air pump/vacuum, based on the design of German engineer Otto Guericke’s vacuum pump in the 1657 book Mechanical Hydraulic Pneumatics by German scientist Gaspar Schott. [1] After conducting a number of experiments with their air pump, Boyle published the results in the 1660 book New Experiments: Physico-Mechanical, Touching the Spring of the Air, and Its Effects (Made for the Most Part in a Pneumatical Engine). In the 1669 second edition of Spring of the Air, a statement of what is now known as "Boyle’s law" can be found defined in modern shorthand as: [2]

which says that for a body of gas at constant number of particles n and temperature T the product of the measure of the pressure P and volume V of gas will be a constant K. The Spring of the Air had a great influence on other scientists, who built their own air pumps, and devised new experiments of their own.

Charles' law
In circa 1787, French scientist Jacques Charles conducted an experiment where he filled five balloons to the same volume with different gases. He then raised the temperature of the balloons to 80ºC and noticed that they all increased in volume by the same amount.

In 1800, an eighteen-year-ear old French chemistry student named Joseph Gay-Lussac, a recent graduate of the École Polytechnique, met and became a lab assistant and protégé of chemist Claude Berthollet. While working under Berthollet, Gay-Lussac discovered that gases expand by the same proportion for an equivalent rise in temperature. Gay-Lussac’s approach to chemistry was to express laws mathematically. [3]

Supposedly, Charles' unpublished experiment was later referenced by Gay-Lussac in 1802 when he published a paper on the precise relationship between the volume and temperature of a gas, which Gay-Lussac named "Charles' Law" in honor of Jacques Charles' original experiment. In modern terms, Charles’ law is define as:

which states that for a body of gas at constant particle number n and pressure P the volume V of the gas will be constant K.

Gay-Lussac’s law
In 1802, French chemist Joseph Gay-Lussac published the results of his findings in what is now known as Gay-Lussac’s law, which in modern terms is:

which states that the pressure P of a body of gas at constant volume V and particle count n will be proportional K to its temperature T.

References
1. (a) Schott, Gaspar. (1657). Mechanical Hydraulic Pneumatics (Mechanicahydraulica-pneumatica). Würtzburg.
(b) Wilson, George. (1849). “On the Early History of the Air-Pump in England”, The Edinburgh New Philosophical Journal, (pgs. 330-54).
2. Morris, Richard. (2005). The Last Sorcerers: the Path from Alchemy to the Periodic Table (pg. 55). The National Academies.
3. Burns, William E. (2003). Science in the Enlightenment: an Encyclopedia (section: Gay-Lussac (1778-1850), pgs. 109-11). ABC-CLIO.

Further reading
● Fox, Robert. (1971). The Caloric Theory of Gases: from Lavoisier to Regnault. Clarendon Press.
● Purrington, Robert D. (1997). Physics in the Nineteenth Century. (section: The Early Gas Laws of Boyle, Mariotte, and Gay-Lussac, pgs. 76-77). Rutgers University Press.