There is a lot of magic smoke inside battery chargers that you do not want to let escape.
- shor circuiting the battery,
- over / under charging...
And you will make mistakes during the design / build of your circuits. Everybody does.
A good Lead-acid battery charger is also a 2 step process:
1). Charge with limited / constant current untill the voltage reaches the maximum.
2). Charge with that voltage until the current drops below a threshold.
The second part is also important to fully charge the battery.
A schmitt trigger can be a part of a battery charger to start / stop the charge process
(Although I woud personally prefer a microcontroller, which also keeps track of (dis) charge currents etc).
Schmitt triggers can be made with even a simple single transistor, but it is easier to understand with an opamp. Start by making a few simple oscillator circuits with opamps. They almost always use a schmitt trigger of some kind. You can generally recognize this by any connection between the output and the non-inverting "+" input of the opamp.
The book "Opamps for everyone" slod006b is a free reference book from Texas Instruments and it is a very good refererence for everything related to opamps.
https://www.eevblog.com/forum/beginners/opamps-for-everyone-pdf/ Then later on in your design you will need some voltage references for the thresholds.
TL431 is a popular choise, but the LM317 (small TO92 ) is also a good candidate.
Chips like these are about a few bucks in a bag of 100 from Ali / Ebay.