The Aqueduct in Mathur is constructed to carry water across the river Parazhiyar(பறளியாறு). It was built in 1966 by the then Chief minister Kamarajar. It is one of the tallest structures as it runs between two small hills with a river in between.
The bus facility is extremely limited. You will need to go to Thiruvattar which is the nearest town. From there you can get to Mathur. However, the frequency of the buses is really low and it is best to come in your vehicle. There is a small entry fee of 5 INR at the time of my visit.
There is a small path along the aqueduct where two people can walk. First you will start at ground level at one of the hills. As you walk forward the depth below will gradually increase and you will see the Parazhiyar below you. At the highest point you can see the surrounding plantations and nearby villages from there. It is an awesome view.
Then you walk all the way to the other end and climb down and come to the river bed. There is a small park near the river banks. You can then cross the river at the nearby road bridge and walk back to where you started. The photo below is taken in the halfway of climbing down.