Alternative to linear regression I'm third year economics student and all econometrics we had so far and basically all empirical studies in economic subjects we had so far are linear regression. Is there any alternative, can anyone suggest any reading material or direction in which I can explore?
There are numerous directions to go which start moving you beyond ordinary least squares (OLS), linear regression. The universe of statistical methods is large! 

Two books that I particularly enjoyed are Econometrics by Hayashi and Elements of Statistical Learning by Hastie et. al. Looking back at your question, these books may be too advanced. But maybe not. An easier version of the latter is An Introduction to Statistical Learning (and may be interesting from the perspective of a broader exposure to data science than just econometrics).


Hayashi's Econometrics introduces a variety of methods through the lens of GMM and with an eye towards time-series econometrics.
Elements of Statistical Learning is a modern classic of the statistics, machine learning literature. It's great for opening your eyes to methods outside of traditional econometrics.


Some examples beyond ordinary least squares...


Maximum likelihood estimation (MLE)

You must know this if you continue doing statistics. It's a ubiquitous workhorse.

If you can specify the likelihood function then parameters of the likelihood function can be estimated by maximizing the likelihood function. In certain special cases, (eg. linear regression with conditionally normal error terms) the OLS estimator is the MLE estimator. You've undoubtedly encountered MLE estimation before if you've estimated a logit model. MLE is all over physics, engineering, and the sciences.

There are issues with applying MLE to economic models though. Often we know that an overall economic model is false. A model will imply certain facts that are entirely fallacious. Forcing the model to match the data in a maximum likelihood sense may not induce a useful choice of parameters. GMM can be used as an alternative approach to selectively test certain predictions of a model.
GMM is another broad method for estimating parameters based upon moment conditions that in expectation should be zero. Hayashi's book Econometrics develops ordinary least squares regression, instrumental variables, maximum likelihood, and other methods as special cases of GMM with different moment conditions. OLS can be thought of as GMM using the orthogonality condition of the regressors and the error terms. MLE can be derived as GMM on the score.

A John Cochrane ode to GMM is here.
Matching methods for estimating causal effects are common in certain areas of economics.

The idea is to match a treated entity with an untreated entity based upon observable characteristics. A widely used technique for example is propensity score matching
There are all kinds of variations on classic linear methods:

The idea here is to start with ordinary least squares but then to bias coefficient estimates towards zero to reduce overfitting and improve out of sample prediction.


Ridge regression
Lasso



References

Fumio, Hayashi, 2000, Econometrics

Hastie, Trevor, Robert Tibshirani, Jerome Friedman, 2009, Elements of Statistical Learning

James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani, 2017, An Introduction to Statistical Learning