The pen tool is a vector drawing tool. Its advantage is that it can draw smooth curves and maintain a smooth effect after scaling or deformation. The vector graphics drawn with the pen tool are called paths. Paths are vector paths that are allowed to be unclosed and open. If the starting point and end point are drawn coincidently, a closed path can be obtained.
Now let's draw a simple path, select the pen tool (shortcut key P) on the toolbar as shown below:

Figure 1
And keep the Pen tool options as shown (above the toolbar): select the second drawing method (simple path) and cancel the rubber band function.

Figure 2
Then click on the screen with a pen, and you will see that there are line segments connecting the hit points. Keep pressing the Shift key to keep the drawn point and the previous point at an angle that is an integer multiple of 45 degrees (such as zero degrees, 90 degrees degrees), so that you can draw horizontal or vertical line segments (the Shift key is pressed starting from the 5th point in the figure).

Figure 3
From the above simple exercise we draw two rules:
We did not draw the line segment directly, but defined the position of each point, and the software connected the points to shape the line. What controls the shape (direction, distance) of the line segment is not the line segment itself, but the position of each point in the line segment. Two terms to remember:
Those points are called anchor points
Line segments between anchor points are called segments
The anchor points we just drew are also called linear anchor points because the line segments between them are straight lines.

Figure 4
Now let's draw the curved anchor point.
We see that when we draw the second and subsequent anchor points and drag the direction line, the shape of the curve also changes.
How are curves generated, and how do we control the shape of the curves? In addition to having the direction and distance of a straight line, the curve has an additional form of curvature. The direction and distance can be achieved by simply changing the position of the anchor point, but how to control the curvature?
As shown in the figure, select the "Direct Selection Tool" on the toolbar and pay attention to the hollow arrow below.

Figure 5
Assume that the four anchor points we just drew are ABCD. Use the "Direct Selection Tool" to select the segment between AB. You will see the direction line we defined when we drew the AB anchor points just now.

Figure 6
Take a closer look at these two directional lines and imagine this:
A person wants to go from point A to point B. When starting from point A, other people at point A see that he is walking in an upward and right direction. The person at point B saw that he was coming downward and to the right. Then combine the observation results from the two places. It can be concluded that the route this person walks: it must be an upper arc similar to a pot lid.
Now we select the "Convert Point Tool" as shown in the picture, which is used to modify the direction line.

Figure 7
Then change the direction line on the AB anchor point as shown in the figure below, and you will see the change in the curvature of the curve. Note that there is a small dot at the end of the direction line. This dot is called the "handle". You have to click on the handle position to change the direction line.

Figure 8
Combined with the metaphor just made, it is not difficult to understand:
Modifying the B anchor point direction line to down is equivalent to specifying that person to start from above point A and enter from below point B, then the distance traveled will be an S shape. Then modify the direction line of anchor point A to downward, which is equivalent to starting from below point A and then entering from below point B. What you are walking is a downward arc. The modified direction line is as shown below:

Figure 9
After understanding the impact of the direction of the direction line on the shape of the curve, let's take a look at the impact of the length of the direction line. As shown below, drag the direction line in the same direction: (You can use the "Direct Selection Tool").

Figure 10
For an anchor point, if the direction line is longer, the distance the curve takes in this direction will be longer, and vice versa. You can imagine that the curve is a rubber band, with two forces pulling in respective directions at the head and tail ends. In whichever direction the force is greater, the rubber band will move closer in that direction. On the contrary.
In addition to modifying the anchor points, you can also use the "Direct Selection Tool" to modify the shape of the curve on the clip. As shown below:

Figure 11
Note: This does not mean "modifying the fragment", but rather "modifying two anchor points at the same time".
Remember the principle: fragments are composed of anchor points. Only by modifying the anchor points can the fragment shape be changed. This is an irreversible cause-and-effect relationship.
Let’s make a summary:
For the two anchor points BC on this curve except the starting point and the end point, there are two direction lines:
One is the "coming" direction line from the previous anchor point; the other is the "going" direction line leading to the next anchor point. For the starting point, there is only the "going" direction line; for the end point, there is only the "going" direction line. direction line.
Let us do a small exercise below, as shown in the figure:

Figure 12
Now you are asked to draw a curve between the two red points that closely follows the outline of the mouse. Most likely what you drew looks like the picture below.

Figure 13
Although the requirement is met, 4 anchor points are used on such a path. Look at the picture below:

Figure 14
The same curve effect is drawn here using only two anchor points. Move the two red dots and draw again. This is probably the effect you draw.

Figure 15
In fact, you only need to use two anchor points to draw this curve, as shown below:

Figure 16
To draw another line in another position, only two anchor points are needed, as shown below:
Remember one rule: the fewer anchor points you have to draw a curve, the better. Because if the number of anchor points increases, it will not only increase the number of drawing steps, but also be unfavorable for later modifications.
At this point, you will definitely have two questions:
Two anchor points seem to be able to cover all curve shapes? This view is obviously wrong. For example, the curve drawn in our first example requires more than two anchor points. So, how to minimize the number of anchor points used?
In fact, there is another question hidden here: Where is the best anchor point? Here are the rules I personally summarized:
The curve shape between two anchor points is divided into two categories: C-shaped and S-shaped.
Several forms of C shape are as follows:

Figure 17
Their direction lines are as follows:

Figure 18
Several forms of S-shaped curves are as follows:

Figure 19
The S-shaped direction line is as shown below:

Figure 20
The animation below demonstrates the dividing point between a C shape and an S shape when adjusting the direction line.

Figure 21
After understanding (and understanding) the shapes of the two curves C and S. You can analyze how many anchor points are needed before drawing. In fact, it is to analyze how many areas can be drawn with a curve (C-shaped or S-shaped).
Although the number of anchor points can reflect the level and proficiency of the drawer. But for most people, just enough to meet their needs is enough. Therefore, when actually drawing, there is no need to be too demanding in reducing the number of anchor points.
Now let's actually draw an M shape, similar to the McDonald's logo. We will introduce three processes, please read the text description clearly first and then watch the animation demonstration. The first method: After completing the drawing, modify the "go" direction line of the second anchor point, and move the anchor point position appropriately. (After drawing, hold down the Ctrl key and click anywhere outside the path to complete the drawing).
Figure 22
Among them we noticed a phenomenon:
When creating a new curve anchor point and dragging its direction line. In fact, as the mouse moves, it is the "going" direction line, and the "coming" direction is always at a 180-degree horizontal angle with it, and the length is also the same. Therefore, although we should originally set the "go" of the second anchor point to the upper right. However, in order to get the "coming direction" correct, we had to set it at the lower right first, and then modify its "going direction" separately after completing the drawing. This method can be described as "throwing it away to keep it coming" (in the same way, it can also be "throwing it around to keep it coming"). It is very inconvenient when drawing a large number of anchor points because the correct curve cannot always be seen.
Now we introduce the second drawing process:
After establishing the second anchor point and defining the direction line according to the "coming direction", modify the "going direction" direction line so that the curve can be drawn correctly. (After drawing, hold down the Ctrl key and click anywhere outside the path to complete the drawing)
Figure 23