How does traceroute work

Here is a very good document which i found from cisco documents.
Have been asked many times in interview

The traceroute command is used to discover the routes that packets actually take when traveling to
their destination. The device (for example, a router or a PC) sends out a sequence of User Datagram
Protocol (UDP) datagrams to an invalid port address at the remote host.
Three datagrams are sent, each with a Time-To-Live (TTL) field value set to one. The TTL value of 1
causes the datagram to "timeout" as soon as it hits the first router in the path; this router then responds
with an ICMP Time Exceeded Message (TEM) indicating that the datagram has expired.
Another three UDP messages are now sent, each with the TTL value set to 2, which causes the second
router to return ICMP TEMs. This process continues until the packets actually reach the other
destination. Since these datagrams are trying to access an invalid port at the destination host, ICMP
Port Unreachable Messages are returned, indicating an unreachable port; this event signals the
Traceroute program that it is finished.
The purpose behind this is to record the source of each ICMP Time Exceeded Message to provide a
trace of the path the packet took to reach the destination.