Though I have been using traditional machine learning algorithms (Regression and Classification) , I have no experience of using Time series and would like to understand what is time series and different approaches(ex:ARIMA,SARIMA,SARIMAX, LSTM etc) used for time series analysis. I also see that people use LSTM's/RNN for time series/sequence classification. Can you people recommend me a book that discusses the above algorithms and how Time series is different from sequence classification etc?
There are numerous topics that you've mentioned but I will suggest those which I've read and are helpful.
For hidden markov models and markov processes I suggest reading Pattern Classification by Richard O. Duda. You can also take a look at Pattern Recognition and Machine Learning by Christopher Bishop. For better understanding Markov processes and their behaviour, you can also take the course stochastic process which is also known as random process. I suggest taking that course before reading any book, because you may need some help if you're not very familiar to the concepts.
LSTMs, I highly suggest taking a look at the fifth course of deep learning on coursera by pr. Andrew Ng. If you do their homework you can realise how the inner operations exactly work and you'll have a very deep understanding of time series and what their nature is. After that, you can take a look at the Deep Learning book by Ian Goodfellow.