Pinsky [1, 2] studied the continuum wavelet, and the integrability conditions of the continuum wavelet kernel, and obtained many useful results using the Fourier transform technique. In the present chapter, integrability conditions of the kernel of the Bessel wavelet transform and its various properties are discussed exploiting the theory of Hankel transform and Hankel convolution. Properties of the partial inverse wavelet transform which is deeply connected with the integrability of the kernel of the Bessel wavelet are also established.