I am from India and whenever we hear about US politics and the US Senate, we always hear about two political parties, Democrats and Republicans. So are these the only two political parties in US? Is the US a dual-party system? And is there a Left-wing or Communist party in the US?
The US is effectively a two party system. While other parties do certainly exist - for example, Jill Stein of the Green Party and Gary Johnson of the Liberterian party were candidates in both the 2012 and 2016 Presidential elections - it is rare, though not completely unheard of (for example, Senator Bernie Sanders is technically an Independent who aligns with the Democrats for procedural reasons), for anyone not representing the two main parties to win public office. This happens largely because the US uses first past the post voting extensively, and is entrenched by the high-profile Presidential election being inherently winner take all. You might want to read this previous answer for a more in depth discussion of how this happens.
However, one notable effect of this, compared to countries like my native Australia, is a lot more voter participation within each party. Candidate preselection via the Primary system provides a very public contest of ideas. Possibly because of this, there is also quite a lot more variance and public disagreement between elected representatives, even from the same party. You might consider these to form a 'mini' multi-party system, although some people do also argue the opposite - that the primary system further entrenches two-party dominance.
There are tons of parties in US politics. However, there are two 'big tent' parties that people fall behind during federal elections. Those being the aformentioned Democrats and Republicans.
There are tons of different parties that are free to operate within the United States. From Communist, to Libertarian (our nations third largest party), all the way to far right groups.
As shown in the other answers, the US is de facto a system where two parties dominate the political scene, and has been for a quite a while. While other parties exist (libertarian, greens, socialist, ...), they usually have a very low representation in chambers.
Dual party systems are usually favored by a system where representatives are chosen with the majority of votes on one geographical area. Indeed, one usually needs to get a huge support in order to get the majority of the votes in a single area (most of the time, 1 seat). Proportional representation on the opposite favors the emergence of many smaller parties, since you can get a good representation without a support close to the majority.
A good illustration of this is given by french legislative elections before and after a change from a proportional representation (IVth republic) to a single winner representation (Vth republic). In 1956, with proportionnal representation, much more parties were allocated a significant number of seats than in 1958, with a majoritarian representation by eletoral areas. You can also usually spot the difference between the French first rounds of presidential elections, and the repartition of seats in the parliament.
There are many other countries which combine proportional and majoritarian representation, for which you can spot the differences in the results.