This paper mainly deals with the tilted Carath$acute{e}$odory class by angle ${lambda}$ ${in}$ ($-{pi}/2$, ${pi}/2$), denoted by $P{lambda}$) an element of which maps the unit disc into the tilted right half-plane {<${omega}$ : Re $e^{i{lambda}}{omega}$ > 0}. Firstly we will characterize $P{lambda}$ from different aspects, for example by subordination and convolution. Then various estimates of functionals over $P{lambda}$ are deduced by considering these over the extreme points of $P{lambda}$ or the knowledge of functional analysis. Finally some subsets of analytic functions related to $P{lambda}$ including close-to-convex functions with argument ${lambda}$, ${lambda}$-spirallike functions and analytic functions whose derivative is in $P{lambda}$ are also considered as applications.