本文主要分为四个部分。第一章是绪论。第二章回顾了Weyl引力及其几何动力学， 此外还讨论了该理论的Noether-Wald荷。 在第三章中，首先讨论了Weyl引力几何动力学中的两个约束，并论证它们是时空度 规共形变换的无穷小生成元。其中一个约束生成空间超曲面的共形变换，而另一个约束 刻画了时空共形变换对超曲面法矢方向的信息。反过来，时空的无穷小共形变换也可以 由这两个约束精确反应出来。接下来我们利用指数映射，讨论了这两个规范生成元对应 的有限变换。我们论证了，它们所生成的有限大变换，是不对易的。这种非对易性来自 两个共形约束之间的Poisson弱对易性。 在第四章中，为了得到联络动力学，我们首先用标架场替代度规场，并由此引入内 部自由度。通过该手段，我们将几何动力学的正则变量重新改写，并引入了新的约束。 接下来，我们论证该形式下约束系统仍然是第一类的。此外，我们论证，额外引入的约 束是内部转动生成元，并且在此标架形式下，其中一个共形约束对正则变量的变换得到 了简化。我们在标架形式的基础上，给出Weyl引力的联络动力学。首先我们将其中一个 变量替换成联络变量，接下来我们改写约束。我们得到了联络动力学的Gauss约束，以及 微分同胚约束，它们类似于引力场耦合物质场的情形。然而Hamiltonian约束的形式仍然 较为复杂。我们还发现，由于理论有两组共轭对，因此存在两种改写正则变量的方式， 它们都不改变原先的辛结构，但是它们的差别可能会在量子动力学中有所体现。

This thesis is constructed in four parts. Chapter 1 is an introduction. In chapter 2 we review the Weyl gravity and its geometrodynamics. In addition, we derive the Noether-Wald charge of this theory. In chapter 3, we firstly discuss two constraints in geometrodynamics of Weyl gravity, and then argue that they are infinitesimal generators of conformal transformations of spacetime metric. One of them generates spatial conformal transformations, and the other encodes information of spacetimes conformal transform on the timelike normal direction. Conversely, an infinitesimal conformal transformation of spacetime metric is exactly reflected by the two constraints. The next step we discuss the finite transformations of the two constraints by employing the exponential maps. We show that, the two finite transformations are noncommunitative. Because of the weak Poisson community of the generators. In chapter 4, we bring triad language into the spatial metric for the sake of going towards connection-dynamical formalism. We firstly substitute the triad field for the metric field, and hence the internal degrees of freedom are introduced. In this manner, we alter the canonical variables in geometrodynamics, and additional constraints are imposed. Then we argue that the first-class property of the constraint algebra is unchanged as the rotation constraint is imposed. Moreover, we show that the additional constraints are the generators of internal rotation, and the transformation generated by one of the conformal constraints is simplified in the triad formalism. Furthermore, based on the triad formalism obtained, we derive the connection dynamical formalism of Weyl gravity. We firstly substitute connection variable for one of original variables. We re-express the constraints by new variables. We obtain the Gauss constraint and diffeomorphism constraint, which are similar to the case of gravitational field coupled to matter field. However, the Hamiltonian constraint is still complicated. In addition, since the theory has two sets of conjugate pairs, we find there exist two alternative for canonical variables. Both of them hold the symplectic structure, but the difference might show out at the quantum dynamical level.