  The Tree Augmentation Problem (TAP) is a fundamental network design problem
in which we are given a tree and a set of additional edges, also called
\emph{links}. The task is to find a set of links, of minimum size, whose
addition to the tree leads to a $2$-edge-connected graph. A long line of
results on TAP culminated in the previously best known approximation guarantee
of $1.5$ achieved by a combinatorial approach due to Kortsarz and Nutov [ACM
Transactions on Algorithms 2016], and also by an SDP-based approach by Cheriyan
and Gao [Algorithmica 2017]. Moreover, an elegant LP-based
$(1.5+\epsilon)$-approximation has also been found very recently by Fiorini,
Gro\ss, K\"onemann, and Sanit\'a [SODA 2018]. In this paper, we show that an
approximation factor below $1.5$ can be achieved, by presenting a
$1.458$-approximation that is based on several new techniques.
