Brush

The Brush Tool allows you to paint in any colour in Photoshop. You can easily change the hardness and softness of the brush, and the opacity and flow of the stroke. However, this is only just the start of what this tool can do.
The Brush Tool can be used with a mouse but really comes into its own when used with a graphics tablet where the size and thickness and flow of the brush can be set to correspond to the pressure exerted with the stylus, which is the way that real brushes, pens and pencils work.
The Brush Settings Window opens up amazing possibilities for creating, modifying and saving your own Custom Brushes, which can behave in the most remarkable ways, such as Hair Brushes. You can also download and install custom brushes made by other people.
Can use any brush on a Path. (See Paths)
Brushes can be used with other Tools, such as the Clone Stamp, Erase Tool, Smudge Tool and Mixer Tool.

More brushes are available with your Photoshop subscription. If you click the gear icon on the top of the Brushes Window it gives you the following links to download more free brushes from Adobe.
Get More Brushes - Takes you to Adobe's website where you can download many more brushes, with new ones added regularly.
Legacy Brushes - Lets you download older versions of Photoshop's default brushes, many of which have been removed from the current default brushes.

Right Click gives brushes dialogue box and ESC hides it.
[ or ] Bracket Keys make the Brush smaller or larger.
SHIFT +[ or ] Bracket Keys make the Brush softer or harder. or larger.
CTRL + OPT+ LEFT MOUSE = Left & Right movement changes brush size and Up & Down movement hardness.
(Also CMD + SPACE + LEFT MOUSE = Zoom image in and out)
Numeric Keys 1 to 0 alter the Opacity, 1=10%, 0=100%, and if you hit the two numbers quickly you can get 55%.
SHIFT + Numeric Keys does the same for Flow.

Pencil Tool - ???
Colour Replacement Tool - ???
Mixer Brush Tool is more like an artist’s brush, in that water can be added to the paint, a small or large amount of paint loaded onto the brush, and even different colours added to the same brush. Explore more ***. Ref,

2018 Update - 01,

Opacity. Clicking on the numbers on the keyboard will change the opacity, so 5 gives 50%, while 0 and 5 pressed quickly one after the other gives 5%. The number 0 makes this 100%. So if you have 50% Opacity one brush stroke will give you 50% Opacity no matter how many times you go over the same area. However, if you paint over an area again with a new brush stroke the density will build up another 50% opacity until you let it go. This way each extra brush stroke does tend to show its edge.
Flow works more like a pencil and the density builds up gradually. Clicking on SHIFT + NUMBER will change the Flow in the same way as Opacity is changed by hitting the numbers directly. Using a low flow allows you to build up a paint layer gradually without brush edges showing because in one brush stroke the paint density builds up each time you pass over an area, until you let the brush go.
Aaron Nace from Phlearn always uses 100% Opacity and only alters the Flow, usually having the flow set to a low value.
If you are on a layer and not the Brush Tool, then the same number shortcuts change the Layer Opacity and the Layer Fill.

Brush Tool