Title: Near Optimal Private and Robust Linear Regression. Abstract: We study the canonical statistical estimation problem of linear regression from $n$ i.i.d. examples under $(\varepsilon,\delta)$-differential privacy when a fraction of response variables are adversarially corrupted.   We propose a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. When there is no adversarial corruption, this algorithm improves upon the existing state-of-the-art approach and achieves near optimal sample complexity. Under label-corruption, this is the first efficient linear regression algorithm to provably guarantee both $(\epsilon,\delta)$-DP and robustness. Synthetic experiments confirm the superiority of our approach. 