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Machine learning, as a subarea of artificial intelligence, is widely believed to reshape the human world in the coming decades. This thesis is focused on both the unsupervised and supervised self-organising transparent machine learning techniques. One particularly interesting aspect is the transparent self-organising deep learning systems. Traditional data analysis approaches and most of the machine learning algorithms are built upon the basis of probability theory and statistics. The solid mathematical foundation of the probability theory and statistics guarantees the good properties of these learning algorithms when the amount of data tends to infinity and all the data comes from the same distribution. However, the prior assumptions of the random nature and same distribution imposed on the data generation model are often too strong and impractical in real applications. Moreover, traditional machine learning algorithms also require a number of free parameters to be predefined. However, without any prior knowledge of the problem, which is often the case in real situations, the performance of the algorithms can be largely influenced by the improper choice. Deep learning-based approaches are currently the state-of-the-art techniques in the fields of machine learning and computer vision. However, they are also suffering from a number of deficiencies including the computational burden of training using huge amount of data, lack of transparency and interpretation, ad hoc decisions about the internal structure, no proven convergence for the adaptive versions that rely on reinforcement learning, limited parallelisation and offline training, etc. These shortcomings largely all hinder the wider applications of the deep learning in real situations. The novel approaches presented in this thesis are developed within the Empirical Data Analytics framework, which is an alternative, but more advanced computational methodology to the traditional approaches based on the ensemble properties and mutual distribution of the empirical discrete observations. The novel self-organising transparent machine learning algorithms presented in this work for clustering, regression, classification and anomaly detection are autonomous, self-organising, data-driven and free from user- and problem- specific parameters. They do not impose any data generation models on the data a priori, but are driven by the empirically observed data and are able to produce the objective results without prior knowledge of the problems. In addition, they are highly efficient and suitable for large-scale static/streaming data processing. The newly proposed self-organising transparent deep learning systems are able to achieve human-level performance comparable to or even better than the deep convolutional neural networks on image classification problems with the merits of being fully transparent, self-evolving, highly efficient, parallelisable and human-interpretable. More importantly, the proposed deep learning systems have the ability of starting classification from the very first image of each class in the same way as humans do. Numerical examples based on numerous challenging benchmark problems and comparisons conducted with the state-of-the-art approaches presented in this thesis demonstrated the validity and effectiveness of the proposed new machine learning algorithms and deep learning systems and show their potential for real applications.