I am working on binary classification of data and I want to know the advantages and disadvantages of using Support vector machine over decision trees and Adaptive Boosting algorithms.
Something you might want to do is use weka, which is a nice package that you can use to plug in your data and then try out a bunch of different machine learning classifiers to see how each works on your particular set. It's a well-tread path for people who do machine learning.
Knowing nothing about your particular data, or the classification problem you are trying to solve, I can't really go beyond just telling you random things I know about each method. That said, here's a brain dump and links to some useful machine learning slides.
Adaptive Boosting uses a committee of weak base classifiers to vote on the class assignment of a sample point. The base classifiers can be decision stumps, decision trees, SVMs, etc.. It takes an iterative approach. On each iteration - if the committee is in agreement and correct about the class assignment for a particular sample, then it becomes down weighted (less important to get right on the next iteration), and if the committee is not in agreement, then it becomes up weighted (more important to classify right on the next iteration). Adaboost is known for having good generalization (not overfitting).
SVMs are a useful first-try. Additionally, you can use different kernels with SVMs and get not just linear decision boundaries but more funkily-shaped ones. And if you put L1-regularization on it (slack variables) then you can not only prevent overfitting, but also, you can classify data that isn't separable.
Decision trees are useful because of their interpretability by just about anyone. They are easy to use. Using trees also means that you can also get some idea of how important a particular feature was for making that tree. Something you might want to check out is additive trees (like MART).
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