Title: Learning Deep ResNet Blocks Sequentially using Boosting Theory. Abstract: We prove a multiclass boosting theory for the ResNet architectures which simultaneously creates a new technique for multiclass boosting and provides a new algorithm for ResNet-style architectures.  Our proposed training algorithm, BoostResNet, is particularly suitable in non-differentiable architectures.  Our method only requires the relatively inexpensive sequential training of T "shallow ResNets". We prove that the training error decays exponentially with the depth T if the weak module classifiers that we train perform slightly better than some weak baseline.  In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition.  A generalization error bound based on margin theory is proved and suggests that ResNet could be resistant to overfitting using a network with l_1 norm bounded weights.