Assumptions of linear regression
There are three major assumptions (statistically strictly speaking):


There is a linear relationship between the dependent variables and the regressors (right figure below), meaning the model you are creating actually fits the data.

The errors or residuals of the data are normally distributed and independent from each other.

Homoscedasticity. This means the variance around the regression line is the same for all values of the predictor variable.



Update 2:: Multicollinearity is not an assumption, but it is rather a sanity check especially if interpretability of the model is important (thanks Ricardo Cruz for the comment). Multicollinearity occurs when the independent variables are not independent from each other. Multicollinearity between explanatory variables which can leads to less stable parameter fits (thanks KT. for pointing this out)). There are tests like correlation matrix (Pearson's Bivariate Correlation), Variance Inflation Factor that can be used to verify this.