Multivariate analysis is a natural extension to univariate analysis and this translation is facilitated by matrix algebra. After a multivariate analysis involving some variables, a study of the individual variables may be necessary in which case univariate analysis will be done on each of the variables of interest. Therefore when the need arises, a combination of the two approaches may be done.  

Yes , this  good answer  but if the varibales in Multivariate case are correlted in this case we can't make individual analysis  on each variable

multivariate analysis is useful for real problems, but to understand multivariate analysis, we need first to understand univariate analysis.

I agree with Dr. Abidy. in multivariate analysis, the covariance structure is important. 

I would say, a multivariate analysis (if this is understood as a multiple regression analysis), should be preceded by the univariate analysis of all independent variables available. As a referee of a paper I always require to see the table of univariates, which is, after all, the first step in any model building strategy towards the final multivariate model. 

And, for good practice, once we know the final multivariate model, we can use the factors that are found to be signficant/important to display/explain the relationships. Very much what we do when we display/explain an interaction with the means plot after a two-way ANOVA (which is essentially a multivariate model).

Univariate Analysis is the fundamental of any analysis as it produces summary of DATA.

Without doing univariate analysis you won't proceed for multivariate as it also helps checking assumptions and other criteria required for multivariate.

Thanks everyone for your marvelous answers.

Meanwhile, is that beneficial to combine univariate analysis and multiple regression analysis ?

multiple regression is models with one dependent variable with some independent variables. Multivariate is models with two/more dependent variable with some independent variables.