In this paper we present the Landmark Model, a model for time series that yields new techniques for similarity-based time series pattern querying. The Landmark Model does not follow traditional similarity models that rely on point-wise Euclidean distance. Instead, it leads to Landmark Similarity, a general model of similarity that is consistent with human intuition and episodic memory.By tracking different specific subsets of features of landmarks, we can efficiently compute different Landmark Similarity measures that are invariant under corresponding subsets of six transformations; namely, Shifting, Uniform Amplitude Scaling, Uniform Time Scaling, Uniform Bi-scaling, Time Warping and Non-uniform Amplitude Scaling.A method of identifying features that are invariant under these transformations is proposed. We also discuss a generalized approach for removing noise from raw time series without smoothing out the peaks and bottoms. Beside these new capabilities, our experiments show that Landmark Indexing is considerably fast.