1. **Problem Statement:** How many lines parallel to line $l$ can be drawn through point $P$? 2. **Understanding the problem:** Line $l$ is given, and point $P$ is not on line $l$. We need to find the number of lines through $P$ that are parallel to $l$. 3. **Key concept:** Through a point not on a given line, there is exactly one line parallel to the given line. This is a fundamental property of parallel lines in Euclidean geometry. 4. **Explanation:** Since $l$ is a line, and $P$ is a point not on $l$, only one line can be drawn through $P$ that does not intersect $l$ and is parallel to it. 5. **Answer:** The number of lines parallel to $l$ through $P$ is $1$. **Final answer:** b. 1